SCERT Maharashtra solutions for Algebra (Mathematics 1) [English] 10 Standard SSC chapter 3 - Arithmetic Progression [Latest edition]

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

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

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For an A.P. 5, 12, 19, 26, … a = ?

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

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

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

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

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

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

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

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 t₅ 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 t₉ = 23 व a = 7

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`

S₁₀₀₀ = `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 t₁ = 1 and t_n = 149 then find S_n.

Activitry :- Here t₁= 1, t_n = 149, S_n = ?

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

= `"n"/2 xx square`

= `square` n, where n = 75

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

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

t_n = a + (n − 1)d

t₁₉ = 9 + (19 − 1) `square`

= 9 + `square`

= `square`

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`

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 S₁₂

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 S₁₀ 

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

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, S₁₀₀ = ?

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

S₁₀₀ = `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, ......

Find S₁₀ 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., t₄ = 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 t₈ = 3 and t₁₂ = 52.

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 t₂₁, if S₄₁ = 4510 in an A.P.

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

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.