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Arithmetic

Progressions

  • Sums based on Sn formula

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6, 12, 18, 24, ...

12) Find the sum of first 40 positive integers divisible by 6.

Sol:

The positive integers which are divisible by 6 are

∴ These numbers form an A.P. with a =

6

and d =

6

Sn =

∴ S40 =

=

=

∴ S40 =

∴ S40 = 4920

Difference between consecutive terms

are same

To find S40

For S40 substitute

n = 40, a = 6 & d = 6

∴ Sum of first 40 positive integers divisible by 6 is 4920.

Exercise 5.3 12

3 of 3

with a = 8 and d = 8

Q.13. Find the sum of the first 15 multiples of 8.

Sol:

The multiples of 8 are

These numbers form an A.P

 

S15 =

 

 

 

 

∴ S15 = 960

∴ Sum of the first 15 multiples of 8 is 960

8, 16, 24, 32…

Difference between consecutive terms

are same

To find S15

 

[2(8) + (15 – 1) 8]

For S15 substitute

n = 15, a = 8 & d = 8

[16 + (14) 8]

[16 + 112]

Exercise 5.3 13

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