Question

The sum of first five terms of an AP and the sum of first seven terms of the same AP is 167. If the sum of first 10 terms of this AP is 235. Find the sum of first 20 terms

Answer 1

Hey

Here is your answer,

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 you!

Answer 2

S7=167
7/2 [2a+6d]=167
2a+6d=167*2/7 (1)
S10=235
5 [2a+9d]=235
2a+9d=235/5=47 (2)
subtracting (2) from (1)
-3d=334/7-47=(334-329)/7=5/7
d=-5/21
2a+9d=47
2a=47-9d
=47+15/7=(329+15)/7=344/7
a=172/7
S20=10 [2*172/7+19 (-5/21)]
=10 [344/7-95/21]
=10 (1032-95)/21
=9370/21