Answer
$a_1=i$
$a_2=-1$
$a_3=-i$
$a_4=1$
$a_5=i$
$S_5=i=\sqrt{-1}$
Work Step by Step
We have to find first five terms of the sequence where
$a_n=i^n, i=\sqrt{-1}$
and $S_{5}.$
$a_1=i^1=i$
$a_2=i^2=-1$
$a_3=i^3=i^2i=-i$
$a_4=i^4=i^2i^2=1$
$a_5=i^5=i^4i=i$
The sequence is:
$i,-1,-i,1,i,-1,-i,1,\cdots$
Calculate $S_5$:
$S_{5}=a_1+a_2+a_3+a_4+a_5=i-1-i+1+i=i=\sqrt{-1}$
