Question

Write the next two terms of the given sequence $-3,1,-5,$ ............. to $17$ terms.

Answer 1

We know the sum of $n$ terms of an A.P with first term $a$ and the common difference $d$ is:

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Here, it is given that the first term is $a=-3$, common difference is $d=1-(-3)=1+3=4$ and $n=17$, therefore, the sum is:

$S_n=\frac{17}{2}\left[\right(2\times -3)+(17-1\left)4\right]=\frac{17}{2}[-6+(16\times 4\left)\right]=\frac{17}{2}(-6+64)=\frac{17\times 58}{2}=17\times 29=493$

Hence, the sum is $493$.