#### Chapters

Chapter 2: Banking (Recurring Deposit Account)

Chapter 3: Shares and Dividend

Chapter 4: Linear Inequations (In one variable)

Chapter 5: Quadratic Equations

Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7: Ratio and Proportion (Including Properties and Uses)

Chapter 8: Remainder and Factor Theorems

Chapter 9: Matrices

Chapter 10: Arithmetic Progression

Chapter 11: Geometric Progression

Chapter 12: Reflection

Chapter 13: Section and Mid-Point Formula

Chapter 14: Equation of a Line

Chapter 15: Similarity (With Applications to Maps and Models)

Chapter 16: Loci (Locus and Its Constructions)

Chapter 17: Circles

Chapter 18: Tangents and Intersecting Chords

Chapter 19: Constructions (Circles)

Chapter 20: Cylinder, Cone and Sphere

Chapter 21: Trigonometrical Identities

Chapter 22: Height and Distances

Chapter 23: Graphical Representation

Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25: Probability

## Chapter 10: Arithmetic Progression

#### Exercise 10(A) [Pages 137 - 138]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise 10(A) [Pages 137 - 138]

Which of the following are in arithmetic progression

2, 6, 10, 14

Which of the following are in arithmetic progression

15, 12, 9, 6

Which of the following are in arithmetic progression

5, 9, 12, 18

Which of the following are in arithmetic progression

`1/2, 1/3 , 1/4 , 1/5`

The nth term of the sequence is (2n – 3), find its fifteenth term.

If the pth term of an A.P. is (2p + 3), find the A.P.

Find the 24th term of the sequence: 12, 10, 8, 6,…

Find the 30th term of the sequence

`1/2, 1, 3/2,....`

Find the 100^{th} term of the sequence:

`sqrt3, 2sqrt3, 3sqrt3......`

Find the 50^{th } term of the sequence:

`1/n, (n + 1)/n, (2n + 1)/n, ....`

Is 402 a term of the sequence:

8, 13, 18, 23.....?

Find the common difference and 99^{th } term of the arthimetic progression:

`7 3/4, 9 1/2, 11 1/4, .....`

How many terms are there in the series:

4, 7, 10, 13, ........,148?

How many terms are there in the series:

0.5, 0.53, 0.56, ......, 1.1?

How many terms are there in the series:

`3/4, 1, 1 1/4, ......, 3`

Which term of the A.P 1 + 4 + 7 + 10 + ..... is 52?

If 5th and 6th terms of an A.P are respectively 6 and 5. Find the 11th term of the A.P

If `t_n` represents n^{th }term of an A.P `t_2 + t_5 - t_3 = 10` and `t_2 + t_9 = 17`. Find its first term and its common difference.

Find the 10th term from the end of the A.P 4, 9, 14, ..... 254

Determine the arithmetic progression whose 3rd term is 5 and 7th term is 9.

Find the 31st term of an A.P whose 10th term is 38 and the 10th term is 74

Which term of the service

21, 18, 15 ...... is -81?

Can any term of this series be zero? if yes find the number of terms.

An A.P. consists of 60 terms, If the first and the last terms be 7 and 125 respectively, find the 31^{st} term.

The sum of the 4^{th} and the 8^{th} terms of an A.P. is 24 and the sum of the 6^{th} and the 10^{th} terms of the same A.P. is 34. Find the first three terms of the A.P.

If the third term of an A.P. is 5 and the seventh term is 9, find the 17^{th} term.

#### Exercise 10(B) [Page 140]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise 10(B) [Page 140]

In an A.P., ten times of its tenth term is equal to thirty times of its 30th term. Find its 40th term.

How many two-digit numbers are divisible by 3?

Which term of A.P. 5, 15, 25 ………… will be 130 more than its 31st term?

Find the value of p, if x, 2x + p and 3x + 6 are in A.P

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, Which term of it is zero?

How many three-digit numbers are divisible by 87?

For what value of n, the nth term of A.P 63, 65, 67, …….. and nth term of A.P. 3, 10, 17,…….. are equal to each other?

Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.

If number n - 2, 4n - 1 and 5n + 2 are in A.P find the value of n and its next two terms.

Determine the value of k for which `k^2 + 4k + 8, 2k^2 + 3k + 6` and `3k^2 + 4k + 4` are in A.P.

If a, b and c are in A.P show that 4a, 4b and 4c are in A.P

If a, b and c are in A.P show that: a + 4, b + 4 and c + 4 are in A.P.

An A.P consists of 57 terms of which 7th term is 13 and the last term is 108. Find the 45th term of this A.P.

4th term of an A.P is equal to 3 times its first term and 7th term exceeds twice the 3rd time by I. Find the first term and the common difference.

The sum of the 2nd term and the 7th term of an A.P is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P

In an A.P, if mth term is n and nth term is m, show that its rth term is (m + n – r)

Which term of A.P 3, 10, 17, .... Will be 84 more than its 13th term?

#### Exercise 10(C) [Pages 143 - 144]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise 10(C) [Pages 143 - 144]

Find the sum of the first 22 terms of the A.P.: 8, 3, -2, ………

How many terms of the A.P: 24, 21, 18, ……… must be taken so that their sum is 78?

Find the sum of 28 terms of an A.P. whose nth term is 8n - 5.

Find the sum of all odd natural numbers less than 50

Find the sum of first 12 natural numbers each of which is a multiple of 7.

Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.

The sum of the first 7 terms of an A.P is 49 and that of the first 17 terms of it is 289. Find the sum of first n terms

The first term of an A.P is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.

Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

In an A.P, the first term is 25, nth term is -17 and the sum of n terms is 132. Find n and the common difference.

If the 8th term of an A.P is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.

Find the sum of all multiples of 7 between 300 and 700.

The sum of n natural number is `5n^2 + 4n`. Find its 8^{th} term.

The fourth term of an A.P. is 11 and the term exceeds twice the fourth term by 5 the A.P and the sum of first 50 terms

#### Exercise 10(D) [Page 146]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise 10(D) [Page 146]

Find three numbers in A.P whose sum is 24 and whoseproduct is 440

The sum of three consecutive terms of an A.P. is 21 and the sum of their squares is 165. find these terms.

The angle of a quadrillateral are A.P. with common difference 20°.find its angles.

Divide 96 into four parts which are in A.P and the ratio between product of their means to product of their extremes is 15:7.

Find five numbers in A.P whose sum is `12 1/2` and the ratio of the first to the last terms 2:3.

Split 207 into three parts such that these partsare in A.P. and the productof the two smaller parts in 4623.

The sum of three numbers in A.P.is 15 the sum of the square of the exterme is 58. find the numbers.

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

Insert one arithmetic mean between 3 and 13.

The angles of a polygon are in A.P. with common differance 5°. if the smallest angle in 120°, find the number ofsides of the polygoa.

`1/a,1/b` and `1/c` are in A.P show that : bc,ca and ab also in A.P.

#### Exercise 10(E) [Page 147]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise 10(E) [Page 147]

Two cars start together in the same direction from the same place. The first cargoes at uniform speed of 10 km h^{-1}. The second car goes at a speed of 8 km h^{-1} in the first hour and thereafter increasing the speed by 0.5 km h^{-1} each succeeding hour. After how many hours will the two cars meet?

A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.

An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installments is Rs. 100 less than the previous one, find :

(i) amount of installments paid in the 9^{th} month

(ii) total amount paid in the installment scheme

A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7^{th} year. Assuming that the production increases uniformly by a fixed number every year find:

(i) the production in the first year.

(ii) the production in the 10^{th} year.

(iii) the total production in 7 years.

Mrs. Gupta repays her total loan of Rs. 1,18,000 by paying installments every month. If the installments for the first month is Rs. 1,000 and it increases by Rs. 100 every month, What amount will she pays as the 30^{th} installments of loan? What amount of loan she still has to pay after the 30^{th} installments

#### Exercise 10(F) [Page 148]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 10 Arithmetic Progression Exercise 10(F) [Page 148]

The 6^{th} term of an A.P. is 16 and the 14^{th} term is 32. Determine the 36^{th} term.

If the third and the 9^{th} term of an A.P. be 4 and -8 respectively, find which term is zero?

An A.P. consists of 50 terms of which 3^{rd} term is 12 and the last term is 106. Find the 29^{th} term of the A.P.

Find the arithmetic mean of:

-5 and 41

Find the arithmetic mean of:

3x - 2y and 3x + 2y

Find the arithmetic mean of:

(m + n)^{2 }and (m - n)^{2}

Find the sum of first 10 terms of the A.P.

4 + 6 + 8 + ……

Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.

How many terms of the series 18 + 15 + 12 + …….. when added together will give 45?

The n^{th} term of a sequence is 8 - 5n. Show that the sequence is an A.P.

Find the general term (n^{th} term) and 23^{rd} term of the sequence 3, 1, -1, -3, ….. .

Which term of the sequence 3, 8, 13, ........ is 78?

Is -150 a term of 11, 8, 5, 2, ....... ?

How many two digit numbers are divisible by 3?

How many multiples of 4 lie between 10 and 250?

The sum of the 4^{th} and the 8^{th} terms of an A.P. is 24 and the sum of the sixth term and the tenth is 44. Find the first three terms of the A.P.

The sum of first 14 terms of an A.P. is 1050 and its 14^{th} term is 140. Find the 20^{th} term.

The 25^{th} term of an A.P. exceeds its 9^{th} term by 16. Find its common difference.

For an A.P., show that:

(m + n)^{th} term + (m - n)^{th} term = 2 × m^{th}term

If the n^{th} term of the A.P. 58, 60, 62,.... is equal to the n^{th} term of the A.P. -2, 5, 12, …., find the value of n.

Which term of the A.P. 105, 101, 97 … is the first negative term?

How many three digit numbers are divisible by 7?

Divide 216 into three parts which are in A.P. and the product of the two smaller parts is 5040.

Can 2n^{2} - 7 be the n^{th} term of an A.P? Explain.

Find the sum of the A.P., 14, 21, 28, …, 168.

The first term of an A.P. is 20 and the sum of its first seven terms is 2100; find the 31^{st} term of this A.P.

Find the sum of last 8 terms of the A.P. -12, -10, -8, ……, 58.

## Chapter 10: Arithmetic Progression

## Selina solutions for Concise Mathematics Class 10 ICSE chapter 10 - Arithmetic Progression

Selina solutions for Concise Mathematics Class 10 ICSE chapter 10 (Arithmetic Progression) 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 CISCE Concise Mathematics Class 10 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 10 ICSE chapter 10 Arithmetic Progression are Arithmetic Progression - Finding Their General Term, Arithmetic Progression - Finding Sum of Their First āNā Terms., Simple Applications of Arithmetic Progression.

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