Question

If $s$${}_n$ denotes the sum of first n terms of an A.P., whose common difference is $d,$ then $s$${}_n$ - 2s${}_{n-1}$ + $s$${}_{n-2}$ $(n>2)$ is equal to

• A. $2d$
• B. $-d$
• C. $d$
• D. None of these

Answer 1

The correct option is C $d$

$s_n-2s_{n-1}+s_{n-2}=(s_n-s_{n-1})-(s_{n-1}-s_{n-2})$

$=a_n-a_{n-1}$ $[\because (s_n-s_{n-1})=a_n]$

$=[a+(n-1\left)d\right]-[a+(n-2\left)d\right]$

$=a+nd-d-a-nd+2d$

$=d$