#### Online Mock Tests

#### Chapters

Chapter 2: Quadratic Equations

▶ Chapter 3: Arithmetic Progression

Chapter 5: Probability

###### Advertisements

###### Advertisements

## Solutions for Chapter 3: Arithmetic Progression

Below listed, you can find solutions for Chapter 3 of Maharashtra State Board SCERT Maharashtra Question Bank for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board.

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

#### MCQ [1 Mark]

**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

**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

**Choose the correct alternative answer for the following sub question**

For an A.P. 5, 12, 19, 26, … a = ?

12

26

19

5

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

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

– 2, 0, 2, 4

– 2, 4, – 8, 16

– 2, – 4, – 6, – 8

– 2, – 4, – 8, – 16

**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

**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

**Choose the correct alternative answer for the following sub-question**

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

30

33

37

38

**Choose the correct alternative answer for the following sub-question**

Find t_{3} = ? in an A.P. 9, 15, 21, 27, ...

27

21

15

9

**Choose the correct alternative answer for the following sub question**

In an A.P., 0, – 4, – 8, – 12, ... find t_{2} = ?

– 8

– 4

– 12

0

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

#### Solve the following sub questions [1 Marks]

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

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

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

Find t_{n} if a = 20 आणि d = 3

Find t_{5} if a = 3 आणि d = −3

t_{n} = 2n − 5 in a sequence, find its first two terms

Find first term of the sequence t_{n} = 2n + 1

Find two terms of the sequence t_{n} = 3n – 2

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

Find d if t_{9} = 23 व a = 7

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

#### Complete the following activity [2 Marks]

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.,

S_{n} = `square`

S_{1000} = `square/2 (1 + 1000)`

= 500 × 1001

= `square`

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

Which term of following A.P. is −940.

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

Activity :- Here a = `square`, d = `square`, t_{n} = −940

According to formula, t_{n} = a + (n − 1)d

−940 = `square`

n = `square`

For an A.P., If t_{1} = 1 and t_{n} = 149 then find S_{n}.

Activitry :- Here t_{1}= 1, t_{n} = 149, S_{n} = ?

S_{n} = `"n"/2 (square + square)`

= `"n"/2 xx square`

= `square` n, where n = 75

t_{19} = ? for the given A.P., 9, 4, −1, −6 ........

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

t_{n} = a + (n − 1)d

t_{19} = 9 + (19 − 1) `square`

= 9 + `square`

= `square`

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

Activity :- Here t_{1} = 7, t_{2} = 14, t_{3} = 21, t_{4} = `square`

t_{2} − t_{1} = `square`

t_{3} – t_{2} = 7

t_{4} – t_{3} = `square`

Therefore, common difference d = `square`

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

#### Solve the following [2 Marks]

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

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

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

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

In an A.P. a = 2 and d = 3, then find S_{12}

Find first four terms of the sequence t_{n} = n + 2

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

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

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

If a = 6 and d = 10, then find S_{10}

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

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

#### Complete the following activity [3 Marks]

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, t_{n} = 95, n = ?

t_{n} = 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

Kalpana saves some amount every month. In the 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, t_{n} = `square`, n = ?

t_{n} = a + (n – 1) `square`

`square` = 100 + (n – 1) × 50

`square/50` = n – 1

n = `square`

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

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

Activity :- Here, a = 12, d = `square`, n = 100, S_{100} = ?

S_{n} = `"n"/2 [square + ("n" - 1)"d"]`

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

= `50(24 + square)`

= `square`

= `square`

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, t_{n} = 136, S_{n} = ?

t_{n} = a + (n – 1)d

`square` = 4 + (n – 1) × 4

`square` = (n – 1) × 4

n = `square`

Now,

S_{n} = `"n"/2["a" + "t"_"n"]`

S_{n} = 17 × `square`

S_{n} = `square`

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

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 n^{th} term of this A.P. be 301

t_{n} = 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, ......

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

#### Solve the following sub questions [3 Marks]

Find S_{10} if a = 6 and d = 3

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

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

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

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?

The n^{th} term of an A.P. 5, 8, 11, 14, ...... is 68. Find n = ?

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

For an A.P., t_{4 }= 12 and its common difference d = – 10, then find t_{n }

Find 27^{th} and n^{th} term of given A.P. 5, 2, – 1, – 4, ......

Find the first terms and common difference of an A.P. whose t_{8} = 3 and t_{12} = 52.

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

#### Solve the following sub questions [ 4 Marks]

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

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

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?

Find the sum of odd natural numbers from 1 to 101

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

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

Find t_{21}, if S_{41} = 4510 in an A.P.

In an A.P. t_{10} = 57 and t_{15} = 87, then find t_{21}

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

Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find S_{n}

## Solutions for Chapter 3: Arithmetic Progression

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

Shaalaa.com has the Maharashtra State Board Mathematics 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. SCERT Maharashtra Question Bank solutions for Mathematics 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Maharashtra State Board 3 (Arithmetic Progression) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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

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

Using SCERT Maharashtra Question Bank 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board solutions Arithmetic Progression exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in SCERT Maharashtra Question Bank Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board students prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exams.

Get the free view of Chapter 3, Arithmetic Progression 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board additional questions for Mathematics 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.