Question

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

Answer 1

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,
$A_1=7+2=9$
$A_2=7+2\left(2\right)=11$
$A_3=7+3\left(2\right)=13$
So, the missing numbers are $9,11$ and $13$.