Question

Find the sum of the first 50 terms.

-6,-2,2,6,...

Answer 1

The common difference is 4. The terms in the series can be written, -6, -6+4, -6+2*4, -6+3*4, ...

When we add the first 50 terms we get 50(-6)=-300 to start and then 4(0+1+2+3+...+49).

The sum of the terms in brackets we can write as (0+49)+(1+48)+(2+47)+...+(24+25)=49+49+49+... 25 times.

So that’s 25*49=1225. So the sum of the first 50 terms is -300+4*1225=-300+4900=4600.

Answer 2

It is an Arithmetic sequence. The common difference is 4.