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 = 35, d=4?

Answer 1

The explicit formula for the sequence is `color(red)( a_n = 4n+31)`, and the first five terms are `color(red)( 35,39,43,47,51)`.

Explanation:

We know that the common difference `d = 4`.

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 = 35 + 4(n-1) = 35 +4n-4`

`a_n = 4n+31`

`a_1 = 35`

`a_2 = 4×2+31 = 8+31 = 39`

`a_3 = 4×3+31 = 12+31 = 43`

`a_4 = 4×4+31 = 16+31= 47`

`a_5= 4×5+31 = 20+31 = 51`

The first five terms are `35,39,43,47,51`.