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

#### Chapters ## Chapter 3: Arithmetic Progression

Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4
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

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

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 the 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 xx 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 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, 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 terms and common difference of an A.P. whose t8 = 3 and t12 = 52.

Q.4

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

#### 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.4 | 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.4 ## SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021 chapter 3 - Arithmetic Progression

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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, Arithmetic Progression, General Term of an Arithmetic Progression, Sum of First n Terms of an A.P., 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.

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