# How do you find the arithmetic means of the sequence 10, __, __, -8?

Jan 10, 2017

Arithmetic sequence is: $10 , 4 , - 2 , - 8$

#### Explanation:

The ${n}^{t h}$ term of an arithmetic sequece s given by:

${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$
Where; ${a}_{1}$ is the first term and $d$ is the common difference.

In this example: ${a}_{1} = 10$ and ${a}_{4} = - 8$

Hence: ${a}_{4} = {a}_{1} + \left(4 - 1\right) \cdot d$

Since ${a}_{1} = 10$ and ${a}_{4} = - 8 \to 10 + \left(4 - 1\right) \cdot d = - 8$

$3 d = - 18$

$d = - 6$

$\therefore {a}_{2} = 10 - 6 = 4$

and

${a}_{3} = 4 - 6 = - 2$

As a check: ${a}_{4} = - 2 - 6 = - 8$

Hence our sequence is: $10 , 4 , - 2 , - 8$