Insert 3 arithmetic means between -27 and 127.

Use a formula and show your work.

-27, _____, _____, _____, 127

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- Dec 3rd 2008, 07:24 AMSteph07Algebra help :( arithmetics
Insert 3 arithmetic means between -27 and 127.

Use a formula and show your work.

-27, _____, _____, _____, 127 - Dec 3rd 2008, 09:06 AMSoroban
Hello, Steph07!

Quote:

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: . $\displaystyle \text{-}27\quad{\color{blue}11.5\quad50\quad88.5}\quad 127$