Question

What is the formula for the following arithmetic sequence?

12, 6, 0, -6, ...


an = 12 + (-6)( n - 1)
an = 12 + 6( n - 1)
an = -6 + 12( n - 1)
an = 6 + 12( n - 1)

and also what would be the 30th term?

Answer 1

`a_(n)` = 12 + (- 6)(n - 1 )

This is an arithmetic sequence with n th term

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

here d = - 6 - 0 = 0 - 6 = 6 - 12 = -6 and
`a_(1)` = 12, hence

`a_(n)` = 12 + (- 6)(n - 1)

use this formula to find the 30 th term

`a_(30)` = 12 + (- 6 × 29) = 12 - 174 = - 162