Question

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

Answer 1

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

Explanation:

The `n^(th)` term of an arithmetic sequece s given by:

`a_n = a_1 + (n-1)*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 + (4-1)*d`

Since `a_1= 10` and `a_4 = -8 -> 10 + (4-1)*d = -8`

`3d=-18`

`d=-6`

`:. 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`