in an AP prove that d=Sn-2Sn-1+Sn-2
Answers
Answered by
1
For an Arithmetic Progression,
S n = 2n
.[2a+(n−1)d]S n−1 = 2n−1
.[2a+(n−2)d] S n−2 = 2n−2
[2a+(n−3)d]
Now, let's take the RHS :
RHS= S n −2S n−1 +S n−2 =an+ 2n(n−1)
.d−2a(n−1)−(n−1)(n−2)d+a(n−2)+ 2(n−2)(n−3)
.d
=a[n−2(n−1)+n−2]+d[
2
n(n−1)
−(n−1)(n−2)+
2
(n−2)(n−3) ]=0+ 2d [(n2 −n)−2(n 2 −3n+2)+(n −5n+6)]
= 2d
(−4+6)= 2d ×2=d =LHS
LHS=RHS
Thus it is proved.
I hope my answer will help you .
Similar questions
Hindi,
2 months ago
English,
2 months ago
Science,
5 months ago
Math,
5 months ago
Environmental Sciences,
9 months ago
Math,
9 months ago
Environmental Sciences,
9 months ago