Question

The sum of the first $20$ terms of the series $-1^2+2^2-3^2+4^2-5^2+6^2.....$ is

• A. $210$
• B. $519$
• C. $190$
• D. $420$
• E. $820$

Answer 1

The correct option is E $820$

We have

$1^2-2^2+3^2-4^2+5^2-6^2..................$

$=(1+2)(1-2)+(3+4)(3-4)+(5+6)(5-6).......$

$=-3+(-7)+(-11)+...........$

The list an A.P with $d=-4$ and $a=-3$

So $S_{20}=\frac{20}{2}\left[2\right(-3)+(20-1\left)\right(-4\left)\right]=820$