A.P

Posted August 3rd, 2008 by alpha

Let S[n] denote the sum of n terms of an A.P whose first term is a .If the common difference d is given by

d=S[n]-kS[n-1]+S[n-2],Then k=?

Comments

On August 3rd, 2008 Structure says:

$a_1=a\:a_2=a+d$

$a_n-a_{n-1}=d$

$s_n=a_1+a_2+...+a_n=s_{n-1}+a_n$

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

$a_n-a_{n-1}+(2-k)s_{n-1}=d+(2-k)s_{n-1}=d$

$2-k=0$

$k=2$