Question

sum of first seven terms of AP is 63 and sum of next seven term is 161 find 28th term

Answer 1

Sum of the first n terms of an A.P, Sn = ( n / 2) [ 2a + ( n -1)d ]

Given that 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)

Also given sum of its next 7 terms is 161.

But 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)

Solving equ (1) and (2) we obtain

d = 2 and a = 3.

Now t28 = a + ( 28 - 1) d

t28 = 3 + ( 28 - 1) 2

t28 = 57.

∴28th term of this A.P. is 57.