Question 1035874
Find the sum of the first 22 terms in the arithmetic series -6 - 12 - 18 - ...

-1,260
-1,518
-1,386
-1,584
~~~~~~~~~~~~~~~~~~~~~~~~~


Use the formula for the sum of the first n terms of an arithmetic progression 


{{{S[n]}}} =  {{{a[1] + a[2] + a[3] + ellipsis + a[n]}}} = {{{(a[1] + (n-1)*d/2)*n}}}


where {{{a[1]}}} is the first term, d is the common difference and n is the number of terms (see the lesson <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A> in this site).


In your case {{{a[1]}}} = -6, d = -6, n = 22.


Plug in this data in the formula and get


{{{S[22]}}} = {{{(-6 + (21*(-6))/2)*22}}}.


Make calculations.