The arithmetic mean of the sequence $7$ , ___, _, ___, $15$ . Find the missing values.

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Solution

Given, $a = 7, b = 15$ and $n = 3$
The common difference for inserting arithmetic means are calculated as $d = \frac{15 - 7}{3 + 1} = 2$
Using the above value of $d$ , the arithmetic means will be,
$A_{1} = 7 + 2 = 9$
$A_{2} = 7 + 2 (2) = 11$
$A_{3} = 7 + 3 (2) = 13$
So, the missing numbers are $9, 11$ and $13$ .

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