Question

Given the arithmetic sequence 8, 5, 2, -1,..., find S20

Answer 1

The formula to find any term of an an arithmetic sequence is given by

`a _(n)`=
`a _(1)`=(n-1)d,
where we have first term
`a_(1)`=8,
and d which is the common difference , and n is the term we need to find (in our case is 20)
the difference d=3, as you see each number is the previous minus 3
for S20=8+(20-1)*(-3)=8+(19)*(-3)=8-57=-49
S20=-49, this the 20th term