Algebra questions

Question

Find the sum of the first 19 terms of the sequence 9, 2, -5, -12, .... Explain each step.

Answer 1

This is an arithmetic sequence where the common difference is -7 ( each term is 7 less than the previous term)

First find the 19th term which is 9+(18)(-7)= 9-126= -117

The sum is the (average of the first and last terms)(number of terms) which is

(9 -117)/2 x 19=-54 x19 = -1026