Question

The sum of 7 terms of A.p. is 63 and the sum of its next 7 terms is 161. find the 28 th term of this A.p.

Answer 1

 Sn = ( n / 2) [ 2a + ( n -1)d 
sum of the first 7 terms of an A.P is 63 i. e S7 = 63.

 ( 7 / 2) [ 2a + 6d ] = 63

 2a + 6d = 18 --------(1)

Sum of its next 7 terms = 161.

 Sum of first 14 terms = sum of first 7 terms + sum of next 7 terms.

S14 = 63 + 161 = 224

 ( 14 / 2) [ 2a + 13d ] = 224.

 7 [ 2a + 13d ] = 224.

⇒ [ 2a + 13d ] = 32 -------92)

By Solving equation (1) and (2) we obtain

d = 2 

 a = 3.

t28 = a + ( 28 - 1) d

t28 = 3 + ( 28 - 1) 2

t28 = 57.

28th term= 57.

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