# NCERT solutions for Mathematics Exemplar Class 10 chapter 5 - Arithematic Progressions [Latest edition]

## Chapter 5: Arithematic Progressions

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4
Exercise 5.1 [Pages 45 - 47]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 5 Arithematic Progressions Exercise 5.1 [Pages 45 - 47]

#### Choose the correct alternative:

Exercise 5.1 | Q 1 | Page 45

In an AP, if d = –4, n = 7, an = 4, then a is ______.

• 6

• 7

• 20

• 28

Exercise 5.1 | Q 2 | Page 45

In an AP, if a = 3.5, d = 0, n = 101, then an will be ______.

• 0

• 3.5

• 103.5

• 104.5

Exercise 5.1 | Q 3 | Page 45

The list of numbers – 10, – 6, – 2, 2, ... is ______.

• An AP with d = – 16

• An AP with d = 4

• An AP with d = – 4

• Not an AP

Exercise 5.1 | Q 4 | Page 45

The 11th term of the AP: -5, (-5)/2, 0, 5/2, .... is ______.

• –20

• 20

• –30

• 30

Exercise 5.1 | Q 5 | Page 45

The first four terms of an AP, whose first term is –2 and the common difference is –2, are ______.

• – 2, 0, 2, 4

• – 2, 4, – 8, 16

• – 2, – 4, – 6, – 8

• – 2, – 4, – 8, –16

Exercise 5.1 | Q 6 | Page 46

The 21st term of the AP whose first two terms are –3 and 4 is ______.

• 17

• 137

• 143

• –143

Exercise 5.1 | Q 7 | Page 46

If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?

• 30

• 33

• 37

• 38

Exercise 5.1 | Q 8 | Page 46

Which term of the AP: 21, 42, 63, 84,... is 210?

• 9th

• 10th

• 11th

• 12th

Exercise 5.1 | Q 9 | Page 46

If the common difference of an AP is 5, then what is a18 – a13?

• 5

• 20

• 25

• 30

Exercise 5.1 | Q 10 | Page 46

What is the common difference of an AP in which a18 – a14 = 32?

• 8

• – 8

• – 4

• 4

Exercise 5.1 | Q 11 | Page 46

Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4th terms is ______.

• –1

• – 8

• 7

• – 9

Exercise 5.1 | Q 12 | Page 46

If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______.

• 7

• 11

• 18

• 0

Exercise 5.1 | Q 13 | Page 46

The 4th term from the end of the AP: –11, –8, –5, ..., 49 is ______.

• 37

• 40

• 43

• 58

Exercise 5.1 | Q 14 | Page 46

The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.

• Pythagoras

• Newton

• Gauss

• Gauss

Exercise 5.1 | Q 15 | Page 46

If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.

• 0

• 5

• 6

• 15

Exercise 5.1 | Q 16 | Page 47

The sum of first 16 terms of the AP: 10, 6, 2,... is ______.

• –320

• 320

• –352

• –400

Exercise 5.1 | Q 17 | Page 47

In an AP if a = 1, an = 20 and Sn = 399, then n is ______.

• 19

• 21

• 38

• 42

Exercise 5.1 | Q 18 | Page 47

The sum of first five multiples of 3 is ______.

• 45

• 55

• 65

• 75

Exercise 5.2 [Pages 49 - 50]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 5 Arithematic Progressions Exercise 5.2 [Pages 49 - 50]

Exercise 5.2 | Q 1.(i) | Page 49

–1, –1, –1, –1, ...

Exercise 5.2 | Q 1.(ii) | Page 49

0, 2, 0, 2, ...

Exercise 5.2 | Q 1.(iii) | Page 49

1, 1, 2, 2, 3, 3,...

Exercise 5.2 | Q 1.(iv) | Page 49

11, 22, 33,...

Exercise 5.2 | Q 1.(v) | Page 49

1/2, 1/3, 1/4, ...

Exercise 5.2 | Q 1.(vi) | Page 49

2, 22, 23, 24,...

Exercise 5.2 | Q 1.(vii) | Page 49

sqrt(3), sqrt(12), sqrt(27), sqrt(48)

Exercise 5.2 | Q 2 | Page 49

Justify whether it is true to say that -1, - 3/2, -2, 5/2, ..... forms an AP as a2 – a1 = a3 – a2.

• True

• False

Exercise 5.2 | Q 3 | Page 49

For the AP: –3, –7, –11, ..., can we find directly a30 – a20 without actually finding a30 and a20? Give reasons for your answer.

• True

• False

Exercise 5.2 | Q 4 | Page 49

Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?

Exercise 5.2 | Q 5 | Page 49

Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer.

Exercise 5.2 | Q 6 | Page 49

The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare (in Rs) after each km is 15, 8, 8, 8, ... Is the statement true? Give reasons.

Exercise 5.2 | Q 7.(i) | Page 49

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers

The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs 400.

Exercise 5.2 | Q 7.(ii) | Page 49

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers

The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250, and it increases by Rs 50 for the next higher class.

Exercise 5.2 | Q 7.(iii) | Page 49

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers

The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.

Exercise 5.2 | Q 7.(iv) | Page 49

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers

The number of bacteria in a certain food item after each second, when they double in every second.

Exercise 5.2 | Q 8.(i) | Page 50

Justify whether it is true to say that the following are the nth terms of an AP.

2n – 3

Exercise 5.2 | Q 8.(ii) | Page 50

Justify whether it is true to say that the following are the nth terms of an AP.

3n2 + 5

Exercise 5.2 | Q 8.(iii) | Page 50

Justify whether it is true to say that the following are the nth terms of an AP.

1 + n + n2

Exercise 5.3 [Pages 51 - 54]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 5 Arithematic Progressions Exercise 5.3 [Pages 51 - 54]

#### Match the APs given in column A with suitable common differences given in column B.

Exercise 5.3 | Q 1 | Page 51
 Column A Column B (A1) 2, – 2, – 6, –10,... (B1) 2/3 (A2) a = –18, n = 10, an = 0 (B2) – 5 (A3) a = 0, a10 = 6 (B3) 4 (A4) a2 = 13, a4 =3 (B4) – 4 (B5) 2 (B6) 1/2 (B7) 5
Exercise 5.3 | Q 2.(i) | Page 52

Verify that the following is an AP, and then write its next three terms.

0, 1/4, 1/2, 3/4, ...

Exercise 5.3 | Q 2.(ii) | Page 52

Verify that the following is an AP, and then write its next three terms.

5, 14/3, 13/3, 4,...

Exercise 5.3 | Q 2.(iii) | Page 52

Verify that the following is an AP, and then write its next three terms.

sqrt(3), 2sqrt(3), 3sqrt(3), ....

Exercise 5.3 | Q 2.(iv) | Page 52

Verify that the following is an AP, and then write its next three terms.

a + b, (a + 1) + b, (a + 1) + (b + 1), ...

Exercise 5.3 | Q 2.(v) | Page 52

Verify that the following is an AP, and then write its next three terms.

a, 2a + 1, 3a + 2, 4a + 3,...

Exercise 5.3 | Q 3.(i) | Page 52

Write the first three terms of the APs when a and d are as given below:

a = 1/2, d = - 1/6

Exercise 5.3 | Q 3.(ii) | Page 52

Write the first three terms of the APs when a and d are as given below:

a = –5, d = –3

Exercise 5.3 | Q 3.(iii) | Page 52

Write the first three terms of the APs when a and d are as given below:

a = sqrt(2), d = 1/sqrt(2)

Exercise 5.3 | Q 4 | Page 52

Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.

Exercise 5.3 | Q 5 | Page 52

Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Exercise 5.3 | Q 6 | Page 52

The 26th, 11th and the last term of an AP are 0, 3 and - 1/5, respectively. Find the common difference and the number of terms.

Exercise 5.3 | Q 7 | Page 52

The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.

Exercise 5.3 | Q 8 | Page 52

Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.

Exercise 5.3 | Q 9 | Page 52

If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term.

Exercise 5.3 | Q 10 | Page 52

Find whether 55 is a term of the AP: 7, 10, 13,--- or not. If yes, find which term it is.

Exercise 5.3 | Q 11 | Page 53

Determine k so that k2 + 4k + 8, 2k2 + 3k + 6, 3k2 + 4k + 4 are three consecutive terms of an AP.

Exercise 5.3 | Q 12 | Page 53

Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Exercise 5.3 | Q 13 | Page 53

The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

Exercise 5.3 | Q 14 | Page 53

If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18,... are the same, find the value of n. Also find that term.

Exercise 5.3 | Q 15 | Page 53

If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is –3, find the 10th term.

Exercise 5.3 | Q 16 | Page 53

Find the 12th term from the end of the AP: –2, –4, –6,..., –100.

Exercise 5.3 | Q 17 | Page 53

Which term of the AP: 53, 48, 43,... is the first negative term?

Exercise 5.3 | Q 18 | Page 53

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

Exercise 5.3 | Q 19 | Page 53

Find the sum of the two middle most terms of the AP: - 4/3, -1, -2/3,..., 4 1/3.

Exercise 5.3 | Q 20 | Page 53

The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Exercise 5.3 | Q 21.(i) | Page 53

Find the sum: 1 + (–2) + (–5) + (–8) + ... + (–236)

Exercise 5.3 | Q 21.(ii) | Page 53

Find the sum: 4 - 1/n + 4 - 2/n + 4 - 3/n + ... upto n terms

Exercise 5.3 | Q 21.(iii) | Page 53

Find the sum: (a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) + .... to 11 terms.

Exercise 5.3 | Q 22 | Page 53

Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77

Exercise 5.3 | Q 23 | Page 53

If an = 3 – 4n, show that 123 a1, a2, a3,... form an AP.

Also find S20

Exercise 5.3 | Q 24 | Page 53

In an AP, if Sn = n(4n + 1), find the AP.

Exercise 5.3 | Q 25 | Page 54

In an AP, if Sn = 3n2 + 5n and ak = 164, find the value of k.

Exercise 5.3 | Q 26 | Page 54

If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 – S4)

Exercise 5.3 | Q 27 | Page 54

Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.

Exercise 5.3 | Q 28 | Page 54

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Exercise 5.3 | Q 29 | Page 54

Find the sum of all the 11 terms of an AP whose middle most term is 30.

Exercise 5.3 | Q 30 | Page 54

Find the sum of last ten terms of the AP: 8, 10, 12,..., 126.

Exercise 5.3 | Q 31 | Page 54

Find the sum of first seven numbers which are multiples of 2 as well as of 9.

Exercise 5.3 | Q 32 | Page 54

How many terms of the AP: –15, –13, –11,--- are needed to make the sum –55? Explain the reason for double answer.

Exercise 5.3 | Q 33 | Page 54

The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is – 30 and the common difference is 8. Find n.

Exercise 5.3 | Q 34 | Page 54

Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?

Exercise 5.3 | Q 35 | Page 54

Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?

Exercise 5.4 [Pages 56 - 58]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 5 Arithematic Progressions Exercise 5.4 [Pages 56 - 58]

Exercise 5.4 | Q 1 | Page 56

The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Exercise 5.4 | Q 2.(i) | Page 57

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

Exercise 5.4 | Q 2.(ii) | Page 57

Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.

Exercise 5.4 | Q 2.(iii) | Page 57

Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

Exercise 5.4 | Q 3 | Page 57

The eighth term of an AP is half its second term and the eleventh term exceeds one-third of its fourth term by 1. Find the 15th term.

Exercise 5.4 | Q 4 | Page 57

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Exercise 5.4 | Q 5.(i) | Page 57

Find the sum of the integers between 100 and 200 that are divisible by 9

Exercise 5.4 | Q 5.(ii) | Page 57

Find the sum of the integers between 100 and 200 that are not divisible by 9

Exercise 5.4 | Q 6 | Page 57

The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Exercise 5.4 | Q 7 | Page 57

Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to ((a + c)(b + c - 2a))/(2(b - a))

Exercise 5.4 | Q 8 | Page 57

Solve the equation – 4 + (–1) + 2 + ... + x = 437

Exercise 5.4 | Q 9 | Page 56

Jaspal Singh repays his total loan of Rs 118000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month, what amount will be paid by him in the 30th instalment? What amount of loan does he still have to pay after the 30th instalment?

Exercise 5.4 | Q 10 | Page 58

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

## Chapter 5: Arithematic Progressions

Exercise 5.1Exercise 5.2Exercise 5.3Exercise 5.4

## NCERT solutions for Mathematics Exemplar Class 10 chapter 5 - Arithematic Progressions

NCERT solutions for Mathematics Exemplar Class 10 chapter 5 (Arithematic Progressions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 10 chapter 5 Arithematic Progressions are Sum of First n Terms of an AP, Derivation of the n th Term, Application in Solving Daily Life Problems, Arithmetic Progressions Examples and Solutions, Arithmetic Progression, General Term of an Arithmetic Progression, nth Term of an AP.

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