Insert 3 arithmetic means between -27 and 127.
Use a formula and show your work.
-27, _____, _____, _____, 127
Hello, Steph07!
Insert 3 arithmetic means between -27 and 127: .$\displaystyle \text{-}27\;\;\_\_\;\;\_\_\;\;\_\_\;\;127$
This is an arithmetic sequence: .first term $\displaystyle a_1 = -27$, number of terms $\displaystyle n = 5$
And we must find the common difference $\displaystyle d.$
We know that: .$\displaystyle a_n \:=\:a_1 + (n-1)d\:\text{ and }\;a_5 = 127$
So we have: .$\displaystyle 127 \:=\:-27 + 4d \quad\Rightarrow\quad d = 38.5$
The five terms are: . $\displaystyle \text{-}27\quad{\color{blue}11.5\quad50\quad88.5}\quad 127$