# Thread: Algebra help :( arithmetics

1. ## Algebra help :( arithmetics

Insert 3 arithmetic means between -27 and 127.
Use a formula and show your work.

-27, _____, _____, _____, 127

2. Hello, Steph07!

Insert 3 arithmetic means between -27 and 127: . $\text{-}27\;\;\_\_\;\;\_\_\;\;\_\_\;\;127$

This is an arithmetic sequence: .first term $a_1 = -27$, number of terms $n = 5$
And we must find the common difference $d.$

We know that: . $a_n \:=\:a_1 + (n-1)d\:\text{ and }\;a_5 = 127$

So we have: . $127 \:=\:-27 + 4d \quad\Rightarrow\quad d = 38.5$

The five terms are: . $\text{-}27\quad{\color{blue}11.5\quad50\quad88.5}\quad 127$