Question

The sum of first $7$ terms of an AP is $10$ and that of next $7$ terms is $17$ .Find the progression.

Answer 1

1, 8/7, 9/7....

Step-by-step explanation:

Let the first term be A and Common difference be D

We know that Sum of n terms = n/2[2a + (n-1)d], where

n = number of terms, a = first term, d = common difference

Given that Sum of first 7 term = 10

∴ 7/2[2A + 6D] = 10

14A + 42D = 20 ----- ( i )

Also,

Sum of Next 7 terms = 17

Sum of next 7 terms will be Sum of 14 terms - Sum of first 7 terms

∴ [14/2(2A + 13D)] - 10 = 17 [Sum of first 7 terms given 10]

7(2A + 13D) = 27

14A + 91D = 27 ------- ( ii )

Subtracting ( i ) from ( ii )

14A + 91D - (14A + 42D) = 27 - 20

49D = 7

D = 1/7

Putting Value of D in ( i )

14A + 42D = 20

14A + 42(1/7) = 20

14A + 6 = 20

14A = 14

A = 1

∴ First Term is 1 and Common Difference is 1/7

∴ AP is 1, 1+1/7, 1+2/7... or 1, 8/7, 9/7....