Advertisement Remove all ads

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 chapter 3 - Arithmetic Progression [Latest edition]

Advertisement Remove all ads

Chapters

10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 - Shaalaa.com

Chapter 3: Arithmetic Progression

Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.
Advertisement Remove all ads
Q.1 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 Chapter 3 Arithmetic Progression Q.1 (A)

MCQ [1 Mark]

Q.1 (A) | Q 1

Choose the correct alternative answer for the following sub question.

In an Arithmetic Progression 2, 4, 6, 8, ... the common difference d is ______

  • 8

  • 6

  • 2

  • – 2

Q.1 (A) | Q 2

Choose the correct alternative answer for the following sub question.

What is the common difference of the sequence 0, – 4, – 8, – 12?

  • 4

  • – 4

  • 8

  • – 8

Q.1 (A) | Q 3

Choose the correct alternative answer for the following sub question

For an A.P. 5, 12, 19, 26, … a = ?

  • 12

  • 26

  • 19

  • 5

Q.1 (A) | Q 4

Choose the correct alternative answer for the following sub questions

A set of numbers where the numbers are arranged in a definite order, like the natural numbers, is called a ______

  • index

  • numbers

  • line

  • sequence

Q.1 (A) | Q 5

Choose the correct alternative answer for the following sub question

First four terms of an A.P., ______ whose first term is – 2 and common difference is – 2

  • – 2, 0, 2, 4

  • – 2, 4, – 8, 16

  • – 2, – 4, – 6, – 8

  • – 2, – 4, – 8, – 16

Q.1 (A) | Q 6

Choose the correct alternative answer for the following sub question

1, 4, 7, 10, 13, ... Next two terms of this A.P. are ______

  • 16, 19

  • 10, 7

  • 19, 22

  • 16, 18

Q.1 (A) | Q 7

Choose the correct alternative answer for the following sub question

Find d of an A.P. whose first two terms are – 3 and 4

  • 7

  • 4

  • – 7

  • – 3

Q.1 (A) | Q 8

Choose the correct alternative answer for the following sub question

If third term and fifth term of an A.P. are 13 and 25 respectively, find its 7th term

  • 30

  • 33

  • 37

  • 38

Q.1 (A) | Q 9

Choose the correct alternative answer for the following sub question

Find t3 = ? in an A.P. 9, 15, 21, 27, ...

  • 27

  • 21

  • 15

  • 9

Q.1 (A) | Q 10

Choose the correct alternative answer for the following sub question

In an A.P., 0, – 4, – 8, – 12, ... find t2 = ?

  • – 8

  • – 4

  • – 12

  • 0

Q.1 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 Chapter 3 Arithmetic Progression Q.1 (B)

Solve the following sub questions [1 Marks]

Q.1 (B) | Q 1

Decide whether the given sequence 2, 4, 6, 8,… is an A.P.

Q.1 (B) | Q 2

Find a and d for an A.P., 1, 4, 7, 10,.........

Q.1 (B) | Q 3

Write the formula of the sum of first n terms for an A.P.

Q.1 (B) | Q 4

Find tn if a = 20 आणि d = 3

Q.1 (B) | Q 5

Find t5 if a = 3 आणि d = −3

Q.1 (B) | Q 6

tn = 2n − 5 in a sequence, find its first two terms

Q.1 (B) | Q 7

Find first term of the sequence tn = 2n + 1

Q.1 (B) | Q 8

Find two terms of the sequence tn = 3n – 2

Q.1 (B) | Q 9

Find common difference of an A.P., 0.9, 0.6, 0.3 ......

Q.1 (B) | Q 10

Find d if t9 = 23 व a = 7

Q.2 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 Chapter 3 Arithmetic Progression Q.2 (A)

Complete the following activity [2 Marks]

Q.2 (A) | Q 1

Find the sum of first 1000 positive integers.

Activity :- Let 1 + 2 + 3 + ........ + 1000

Using formula for the sum of first n terms of an A.P.,

Sn = `square`

S1000 = `square/2 (1 + 1000)`

= 500 × 1001

= `square`

Therefore, Sum of the first 1000 positive integer is `square`

Q.2 (A) | Q 2

Which term of following A.P. is −940.

50, 40, 30, 20 ........

Activity :- Here a = `square`, d = `square`, tn = −940

According to formula, tn = a + (n − 1)d

−940 = `square`

n = `square`

Q.2 (A) | Q 3

For an A.P., If t1 = 1 and tn = 149 then find Sn.

Activitry :- Here t1= 1, tn = 149, Sn = ?

Sn = `"n"/2 (square + square)`

= `"n"/2 + square`

= `square` n, where n = 75

Q.2 (A) | Q 4

t19 = ? for the given A.P., 9, 4, −1, −6 ........

Activity :- Here a = 9, d = `square`

tn = a + (n − 1)d

t19 = 9 + (19 − 1) `square`

= 9 + `square`

= `square`

Q.2 (A) | Q 5

Common difference, d = ? for the given A.P., 7, 14, 21, 28 ........

Activity :- Here t1 = 7, t2 = 14, t3 = 21, t4 = `square`

t2 − t1 = `square`

t3 – t2 = 7

t4 – t3 = `square`

Therefore, common difference d = `square`

Q.2 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 Chapter 3 Arithmetic Progression Q.2 (B)

Solve the following [2 Marks]

Q.2 (B) | Q 1

Decide whether the following sequence is an A.P. or not.

3, 5, 7, 9, 11 ........

Q.2 (B) | Q 2

Find first four terms of an A.P., whose first term is 3 and common difference is 4.

Q.2 (B) | Q 3

1, 6, 11, 16 ...... Find the 18th term of this A.P.

Q.2 (B) | Q 4

In an A.P. a = 2 and d = 3, then find S12

Q.2 (B) | Q 5

Find first four terms of the sequence tn = n + 2

Q.2 (B) | Q 6

In an A.P., a = 10 and d = −3 then find its first four terms

Q.2 (B) | Q 7

1, 7, 13, 19 ...... find 18th term of this A.P.

Q.2 (B) | Q 8

In an A.P. a = 4 and d = 0, then find first five terms

Q.2 (B) | Q 9

If a = 6 and d = 10, then find S10 

Q.2 (B) | Q 10

Decide whether the given sequence 24, 17, 10, 3, ...... is an A.P.? If yes find its common term (tn)

Q.3 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 Chapter 3 Arithmetic Progression Q.3 (A)

Complete the following activity [3 Marks]

Q.3 (A) | Q 1

How many two-digit numbers are divisible by 5?

Activity :-  Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.

Here, d = 5, therefore this sequence is an A.P.

Here, a = 10, d = 5, tn = 95, n = ?

tn = a + (n − 1) `square`

`square` = 10 + (n – 1) × 5

`square` = (n – 1) × 5

`square` = (n – 1)

Therefore n = `square`

There are `square` two-digit numbers divisible by 5

Q.3 (A) | Q 2

Kalpana saves some amount every month. In first three months she saves ₹ 100, ₹ 150 and ₹ 200 respectively. In how many months will she save ₹ 1200?

Activity :- Kalpana’s monthly saving is ₹ 100, ₹ 150, ₹ 200, ......, ₹ 1200

Here, d = 50.Therefore this sequence is an A.P.

a = 100, d = 50, tn = `square`, n = ?

tn = a + (n – 1) `square`

`square` = 100 + (n – 1) × 50

`square/50` = n – 1

n = `square`

Therefore, she saves ₹ 1200 in `square` months.

Q.3 (A) | Q 3

Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......

Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?

Sn = `"n"/2 [square + ("n" - 1)"d"]`

S100 = `square/2 [24 + (100 - 1)"d"]`

= `50(24 + square)`

= `square`

= `square`

Q.3 (A) | Q 4

Find the sum of natural numbers between 1 to 140, which are divisible by 4.

Activity :- Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16, ......, 136

Here d = 4, therefore this sequence is an A.P.

a = 4, d = 4, tn = 136, Sn = ?

tn = a + (n – 1)d

`square` = 4 + (n – 1) × 4

`square` = (n – 1) × 4

n = `square`

Now,

Sn = `"n"/2["a" + "t"_"n"]`

Sn = 17 × `square`

Sn = `square`

Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`

Q.3 (A) | Q 5

Decide whether 301 is term of given sequence 5, 11, 17, 23, .....

Activity :-  Here, d = `square`, therefore this sequence is an A.P.

a = 5, d = `square`

Let nth term of this A.P. be 301

tn = a + (n – 1) `square`

301 = 5 + (n – 1) × `square`

301 = 6n – 1

n = `302/6` = `square`

But n is not positive integer.

Therefore, 301 is `square` the term of sequence 5, 11, 17, 23, ......

Q.3 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 Chapter 3 Arithmetic Progression Q.3 (B)

Solve the following sub questions [3 Marks]

Q.3 (B) | Q 1

Find S10 if a = 6 and d = 3

Q.3 (B) | Q 2

12, 16, 20, 24, ...... Find 25th term of this A.P.

Q.3 (B) | Q 3

If tn = 2n – 5 is the nth term of an A.P., then find its first five terms

Q.3 (B) | Q 4

Find the sum of three-digit natural numbers, which are divisible by 4

Q.3 (B) | Q 5

Merry got a job with salary ₹ 15000 per month. If her salary increases by ₹ 100 per month, how much would be her salary after 20 months?

Q.3 (B) | Q 6

The nth term of an A.P. 5, 8, 11, 14, ...... is 68. Find n = ?

Q.3 (B) | Q 7

What is the sum of an odd numbers between 1 to 50?

Q.3 (B) | Q 8

For an A.P., t4 = 12 and its common difference d = – 10, then find tn 

Q.3 (B) | Q 9

Find 27th and nth term of given A.P. 5, 2, – 1, – 4, ......

Q.3 (B) | Q 10

Find the first term and common difference of an A.P. whose t8 = 3 and t12 = 52

Q.4, Q.

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 Chapter 3 Arithmetic Progression Q.4, Q.

Solve the following sub questions [ 4 Marks]

Q.4 | Q 1

Sum of first 55 terms in an A.P. is 3300, find its 28th term.

Q.4 | Q 2

Find the sum of numbers between 1 to 140, divisible by 4

Q.4 | Q 3

In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?

Q.4 | Q 4

Find the sum of odd natural numbers from 1 to 101

Q.4 | Q 5

Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years

Q.4 | Q 6

A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment

Q.4 | Q 7

Find t21, if S41 = 4510 in an A.P.

Q.4 | Q 8

In an A.P. t10 = 57 and t15 = 87, then find t21 

Q. | Q 9

If ₹ 3900 will have to be repaid in 12 monthly instalments such that each instalment being more than the preceding one by ₹ 10, then find the amount of the first and last instalment

Q.4 | Q 10

Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn 

Chapter 3: Arithmetic Progression

Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.
10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 chapter 3 - Arithmetic Progression

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 chapter 3 (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 Maharashtra State Board 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. SCERT Maharashtra Question Bank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 chapter 3 Arithmetic Progression are Introduction to Sequence, Arithmetic Progressions Examples and Solutions, Terms in a sequence, Geometric Mean, Arithmetic Progression, Geometric Progression, General Term of an Arithmetic Progression, General Term of an Geomatric Progression, Sum of First n Terms of an AP, Sum of the First 'N' Terms of an Geometric Progression, Arithmetic Mean - Raw Data, Concept of Ratio.

Using SCERT Maharashtra Question Bank 10th Standard [इयत्ता १० वी] solutions Arithmetic Progression exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 10th Standard [इयत्ता १० वी] prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 3 Arithmetic Progression 10th Standard [इयत्ता १० वी] extra questions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 and can use Shaalaa.com to keep it handy for your exam preparation

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×