Question

How do you write a rule for the nth term of the arithmetic sequence `a_7=21, a_13=42`?

Answer 1

`a_n = 7/2(n-1)`

Explanation:

Arithmetic sequence, `a_n = a_1 + (n-1)d`, d=common difference.

given that,
`a_7 = 21`
`a_1 + (7-1)d = 21`
`a_1 + 6d = 21 ->`A

`a_13 = 42`
`a_1 + 12d = 42->`B

B-A,
`6d =21` `->d =21/6 = 7/2`

Plug in `d = 7/2` in A or B.
`a_1 + 6(7/2) = 21`
`a_1 + 21 = 21` `->a_1 = 0`

therefore,
`a_n = 0 + (n-1)7/2`
`a_n = 7/2(n-1)`