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  • Sums based on ‘an’ Formula

ARITHMETIC

PROGRESSIONS

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12) Two APs have the same common difference. The difference

between their 100th terms is 100, what is the difference between

their 1000th terms?

Sol:

We need to find A1000 – a1000

Let d be the common difference of both APs.

and first term be denoted by ‘A’ and ‘a’

of two APs respectively.

A100 – a100

∴ A + 99d

–

(a + 99d)

= 100

∴ A + 99d

–

a – 99d

= 100

∴ A – a

= 100

…..(i)

A1000 – a1000

= A + 999d

–

(a + 999d)

= A + 999d

–

a – 999d

= A – a

= 100

….. (from i)

Lets find A1000 – a1000

∴ Difference between their 1000th terms is 100.

= 100

A100 = A + 99d

a100 = a + 99d

Exercise 5.2 12