Question

How do you find the arithmetic means of the sequence 55, __, __, __, 115?

Answer 1

Arithmetic Mean = `color(green)(85)`

Explanation:

Suppose the common difference is `d`
Then the first 5 terms are
[1] `a =55`
[2] `a+d=55+d`
[3] `a+2d=55+2dcolor(white)("XX")larr "middle term"`
[4] `a+3d=55+3d`
[5] `a+4d=55+4d=115`

Since `55+4d=115`
`rarr 4d=60`

`rarr d=15`

The arithmetic means (average) of an arithmetic sequence with an odd number of terms is the value of the middle term.
In this case,
`"Average" = a+2d = 55+2 * 15 = 55+30 =85`