Question

If Sn denotes the sum of n terms of an AP whose common difference is d and first term is a.Find Sn-2Sn-1+Sn-2

Answer 1

is there is a comma between the numbers which we have to find

Answer 2

Answer:

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

Step-by-step explanation:

Given : If Sn denotes the sum of n terms of an AP whose common difference is d and first term is a.

To Find : $S_n-2S_{n-1}+S_{n-2}$

Solution :

We know that,

nth term of A.P is  $T_n=S_n-S_{n-1}$

(n-1)th term of A.P is  $T_{n-1}=S_{n-1}-S_{n-2}$

Common difference is nth term - (n-1)th term

i.e. $d=T_n-T_{n-1}$

Now,

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

Split the middle term,

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

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

Substitute,

$=(T_n)-(T_{n-1})$

Substitute the value,

$=d$

Therefore,  $S_n-2S_{n-1}+S_{n-2}=d$