Question

if the sum of first 8 term of an ap is 64 and that of 18 terms is 324 find the sum of first n terms

Answer 1

Hope it helps mate:)

Answer 2

S8=8/2(2a+7d)=64
=8a+28d=64
=4(2a+7d)=64
2a+7d=64/4
2a+7d=16
7d=16-2a
d=16-2a/7___eqn(1)

S18=18/2(2a+17d)=324
=9(2a+17d)=324
2a+17d=36
2a+(16-2a/7)=36 (from eqn (1))
14a+16-2a/7=36
16a+16=252
16(a+1)=252
a+1=252/16
a=252/16-1
a=252-16/16
a=236/16



now put value of a in eqn (1)

d=16-2(236/16)/7
d=16-472/16×7
d=-456/16×7
d=-3192/16


now,
Sn=n/2{2(236/16)+(n-1)-3192/16=0
=n/2(236/8+(n-1)-3192/16=0
=236n/8+n^2-n-3192n/16=0
=472n+16n^2-16n-3192n/16=0
=456n-3192n+16n^2=0
16n^2-2736=0
16n(n-171)=0
value of n is either 0 or 171 answer