Question

the sum of first 9 terms of an Ap is 171 and that for the first 24 terms is 996. find the first term and the common difference

Answer 1

Given,

S9=171

S24=996

Sn=n/2(2a+(n-1)d)

S9=9/2(2a+(9-1)d)

171=9/2(2a+8d)

171=9(a+4d)

a+4d=19-------(1)

Similarly,

S24=12(2a+23d)

276=12(2a+23d)

2a+23d=23---------(2)

From equation (1) and (2), we get

d= -1 and a=23