Question

Find the arithmetic mean of the AP $2,4,6,8,...20.$

• A. 9
• B. 10
• C. 10.5
• D. 11

Answer 1

The correct option is D 11

For the given AP, $a=2$ and $d=4-2=2$

AM of an AP $=\frac{\text{Sum of terms}}{\text{Number of terms}}$
$=\frac{\frac{n}{2}\times [2a+(n-1\left)d\right]}{n}$
$=a+\frac{(n-1)d}{2}$...........(1)

Let, 20 be the $n^{th}$ term.

$\Rightarrow 20=2+(n-1)2$

$\Rightarrow n=10$

Substituting n in the eq(1), we get:

$\text{AM}=2+\frac{9\times 2}{2}$
$=11$
$\therefore$ Arithmetic mean of the given series is 11.