Question

In any A.P., $S_n-2S_{n-1}+S_{n-2}=.....(n>2)$

• A. $a+d$
• B. $2d$
• C. $d$
• D. $a$

Answer 1

The correct option is C $d$

We know that, $T_n=S_n-S_{n-1}$, where $S_n$ is sum of first $n$ terms

$S_n-2S_{n-1}+S_{n-2}$

$=S_n-S_{n-1}-S_{n-1}+S_{n-2}$

$=(S_n-S_{n-1})-(S_{n-1}-S_{n-2})$
$=T_n-T_{n-1}=d$

Hence, $S_n-2S_{n-1}+S_{n-2}=d$