Question

What is the 52nd term for the following sequence ? 14,6,-2,-10,-18

Answer 1

`a_(52)` = - 394

Explanation:

these are the terms of an arithmetic sequence with nth term

`a_(n)` =
`a_(1)` + (n - 1)d

where d is the common difference and
`a_(1)` the first term

d = - 18 - (- 10) = - 10 - (- 2) = - 2 - 6 = - 8 and
`a_(1)` = 14, hence

`a_(52)` = 14 + (51 × - 8) = 14 - 408 = - 394