Question

Find the arithmetic means in each sequence.

-8, ? , ? , ?, ? , 7

Short answer

The arithmetic means in the sequence are-5, -2, 1, 4.

Step-by-step solution

Step 1. Given Information.

Given there are four arithmetic means between -8 and 7.

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$.

Since there are four arithmetic means between -8 and 7,

The first term is $a_1=-8$

And the sixth term is $a_6=7$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_6=a_1+(6-1)d\\ 7=-8+5d\\ 5d=7+8\\ 5d=15\\ d=3\end{array}$

Hence the common difference is 3.

Since the first term in the arithmetic sequence is -8:

The next term in the arithmetic sequence is $-8+3=-5$

The next term in the arithmetic sequence is $-5+3=-2$

The next term in the arithmetic sequence is $-2+3=1$

The next term in the arithmetic sequence is $1+3=4$

And the sixth term in the arithmetic sequence is 7.

Step 3. Conclusion.

Hence, the arithmetic means in the sequence are -5, -2, 1, 4.