Question

What is the explicit formula for this arithmetic sequence?
-12,-17, -22, -27, ...

Answer 1

Explanation:

An explicit arithmetic formula in standard form is

`A_n=a_1+d(n-1)` where n is the position of a number in thesequence, a1 is the first number in the given sequence, and d is the common difference. The common diff here is -5 since we have to subtract 5 from each term to get to the next one in the sequence. The first number is -12. So

a1 = -12

d = -5 and the explicit formula is

`A_n=-12-5(n-1)` and you could simplify it a bit to

`A_n=-12-5n+5` and finally to

`A_n=-5n-7` which is a linear representation. Arithmetic sequences can all be simplified down to represent lines.