Question

If a, b, c, d, e, f are AMs between 2 and 12 then find the sum a+b+c+d+e+f

Answer 1

42

Answer 2

The sum of $n$ arithmetic means inserted between two numbers $A$ and $B$ is given by $n \times \frac{A+B}{2}$. Here, $A=2$, $B=12$, and $n=6$. Therefore, the sum is $6 \times \frac{2+12}{2} = 6 \times \frac{14}{2} = 6 \times 7 = 42$.