Question

The sum of first five terms of an ap and the sum of first 7 terms of an ap is 167 if the sum of first 10 terms of AP is 35 find sum of AP

Answer 1

S₅=S₇

and S₇=S₅+6th term

S₅=S₅+6th term

6th term=0

a+5d=0

2a+10d=0--------eq1

S₁₀=235

n/2(2a+(n-1)d)=235

10/2(2a+9d)=235

2a+9d=47--------eq2

on subtracting eq2 from eq1 we get

d=-47

a=235

S₂₀=20/2(2(235)+19(-47))

S₂₀=10(470-893)

S₂₀=-4230

Hope it helps:)