Question

The sum of first 8 terms of an a.p is 140 and the sum of first 24 terms is 996. Find the a.p.

Answer 1

We know,
Sn = n/2{2a + (n -1)d}
A/C to question ,
S8 = 140 ,
140 = 8/2{2a + (8-1)d }
140 = 4{2a + 7d }
35 = 2a + 7d ----------(1)

again,
S24 = 996
996 = 24/2 { 2a + (24-1)d }
996 = 12(2a + 23d )
83 = 2a + 23d -------(2)
subtract eqn (2) -(1)

48 = 16d
d = 3 put this in eqn (1)
a = 7
hence, AP : 7, 10, 13 , 16 .......