Question

The sum of the first 5 terms and the sum of the first 11 terms of an AP is 167 if the sum of the first 10 terms of this AP is 235 then find the sum of its first 20 terms.

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))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