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 28^th term of this A.P.

Answer 1

S₇ = 63 

\(\frac{7}{2}\)[2(a) + 6d] = 639 

a + 3d = 9 (i)

a₈ = a + 7d

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

Sum of next 7 terms, S’₇ = \(\frac{7}{2}\)[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