Question

If the 6th term of an arithmetic sequence is

12 and the 15th term is -15, find the first
term and the common difference.

Answer 1

d = -3

`a_(1)` = 27

Explanation:

You have to use the formula
`a_(n) = a_(1) + (n - 1)d` two times, once for the 6th term and once for the 15th term

(1)
`12 = a_(1) + (6 - 1)d` (2)
`-15 = a_(1) + (15 - 1)d`

`12 = a_(1) + 5d`
`-15 = a_(1) + 14d` Change signs and add to (1)

`15 = - a_(1) - 14d`

27 = -9d

d = -3 - 15 =
`a_(1)` + 14(-3)

- 15 =
`a_(1)` - 42

`a_(1)` = 27