Question

Let Sn denote the sum of n terms of an AP whose first term is a. if the common difference d is given by d = Sn - KSn-1 + Sn-2 .then k

Answer 1

HELLO DEAR,

Given, Sn denote the sum of n terms and d is the common difference of the A.P.

nth term of the A.P., $\bold{a_n = S_n - S_{n - 1}}$----------( 1 )

Common difference of A.P., $\bold{d = a_n - a_{n - 1}}$ --------( 2 )

Now,

Replacing n by (n - 1) in -------( 1 ),

we get

$\bold{a_{n - 1} = S_{n - 1} - S_{(n - 1) - 1}}$

$\bold{a_{n - 1} = S_{n - 1} - S_{n - 2}}$ ----------( 3 )

So, there is two successive terms

then, d = $\bold{a_{n} - a_{n - 1}}$

from---------( 1 ) &----------( 3 )

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

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

$\bold{d = s_n - 2s_{n - 1} - s_{n - 2}}$----------( 4 )

Now, from the given value of d in the question is :- $\bold{d = s_n - ks_{n - 1} - s_{n - 2}}$

from-------( 4 )

$\bold{s_n - 2s_{n - 1} - s_{n - 2} = s_n - ks_{n - 1} - s_{n - 2}}$

$\bold{\large{\boxed{HENCE, \;\;THE\;\; VALUE\;\;OF\;\;K = 2}}}$

I HOPE ITS HELP YOU DEAR,

THANKS

Answer 2

Answer:

Step-by-step explanation: