Question

Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 28, d=10?

Answer 1

The explicit formula for the sequence is `color(red)( a_n = 10n+18)`, and the first five terms are `color(red)( 28,38,48,58,68)`.

We know that the common difference `d = 10`.

The general formula for an arithmetic sequence is

`a_n = a_1 + (n-1)d`.

So, for your sequence, the general formula is

`a_n = 28 + 10(n-1) = 28 +10n-10`

`a_n = 10n+18`

`a_1 = 28`

`a_2 = 10×2+18 = 20+18 = 38`

`a_3 = 10×3+18 = 30+18 = 48`

`a_4 = 10×4+18 = 40+18 = 58`

`a_5 = 10×5+18 = 50+18 = 68`

The first five terms are `28,38,48,58,68`.