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= -34, d=-10?

Answer 1

The explicit formula for the sequence is `color(red)( a_n = -10n-24)`, and the first five terms are `color(red)(-34, -44, -54, -64, -74)`.

Explanation:

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 = -34 + (n-1)(-10) = -34 -10n+10`

`a_n = -10n-24`

`a_1 = -34`

`a_2 = -10×2-24 = -20-24 = -44`

`a_3 = -10×3-24 = -30-24 = -54`

`a_4 = -10×4-24 = -40-24 = -64`

`a_5 = -10×5-24 = -50-24 = -74`

The first five terms are `-34, -44, -54, -64, -74`.