Question

The second and fourth terms of a sequence are 64 and 100. If the sequence is arithmetic, write an equation for

the nth term.

Answer 1

If d is the common difference between consecutive terms, then

`a_4 = a_3 + d = a_2 + 2d`

We have
`a_2 = 64` and
`a_4 = 100`, so

`a_4 - a_2 = 100 - 64 = 36 = 2d \implies d = 18`

Then the 1st term in the sequence is

`a_2 = a_1 + d \implies 64 = a_1 + 18 \implies a_1 = 46`

and the n-th term would be

`a_n = a_1 + (n-1) d \implies a_n = 46 + 18 (n-1) \implies \boxed{a_n = 18n + 28}`