Question

if the sum of first 7 terms of an AP is 63 and the sum of next 7 terms is 161 find the 28th term of the AP

Answer 1

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Answer 2

hey......

Sum of first n term of an A.P =

= n / 2 [ 2a + ( n - 1 )d ]

Given :-

S7 = 63

7 / 2 [ 2a + 6d ] = 63

2a + 6d = 18 .................. ( 1 )

Also , Sum of next 7 term is 161. Thus , Sum of first 14 term = Sum of the first 7 term + Sum of next 7 term

S14 = 63 + 161 = 224

14 / 2 [ 2a + 13d ] = 224

2a + 13d = 32. ................. ( 2 )

Solving equation ( 1 ) and ( 2 ) , we get ,

a = 3 and d = 2

Therefore ,

T28 = a + ( 28 - 1 )d

T28 = 3 + 27 × 2

T28 = 3 + 54 = 57

Hence, 28th term of the A.P. is 57..
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