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 28^th term of this A.P.

S₇ = 63

[2(a) + 6d] = 639

(i)

Hence, for next 7 terms first term will be the 8^th term i.e. a + 7d

Sum of next 7 terms, S’₇ = [2(a + 7d) + 6d]

161 = 7 [a + 7d + 3d]

23 = a + 10d

23 = 9 – 3d + 10d [From (i)]

14 = 7d

d = 2

Putting the value of d in (i), we get

A = 9 – 3(2) = 3

Now, a₂₈= a + 27d

= 3 + 27(2)

= 3 + 54 = 57