Question

Find the general term and the sum of n terms of the series $2,5,12,31,86,....$

Answer 1

$\Rightarrow 251231\mathrm{86....}$

$3719\mathrm{55....}$

$412\mathrm{36....}$

$\therefore u_n=a.3^{n-1}+bc+c$

Putting $n=1,2,3,$ we get;-

$a=1,b=1,c=0$

$u_n=3^{n-1}+n$

$S_n=\sum u_n$

$S_n=\frac{1}{2}(3^n-1)+\frac{n(n+1)}{3}$

$=\frac{3^n+n^2+n-1}{2}$