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Question

The sum of the first 7 terms of an A.P is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

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Solution

Sum of first n terms of an A.P.=n2[2a+(n1)d]

Given:
S7=63
72[2a+6d]=63
2a+6d=18 ...... (1)

Also, sum of next 7 terms is 161. Thus,
Sum of first 14 terms = Sum of first 7 terms + Sum of next 7 terms
S14=63+161=224
142[2a+13d]=224
2a+13d=32 ...... (2)

Solving equations (1) and (2), we get,
a=3 and d=2

Therefore,
T28=a+(281)d
T28=3+27×2
T28=3+54=57

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

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