Question

Find the arithmetic mean of the series $1,3,5,...........(2n-1)$

• A. $n$
• B. $2n$
• C. $n/2$
• D. $n-1$

Answer 1

The correct option is A $n$

In the given Arithmetic Progression,
First term $=a=1$
Common difference $=3-1=2$
Let $2n-1$ be the $k$ th term.
Then $x_n=a+(n-1)d$
$=>2n-1=1+(k-1)2$
$=>2n-1=1+2k-2$
$=>k=n$
So, $2n-1$ is the $n$ th term.
Now, Sum of the given series upto 'n' terms $=\frac{n}{2}(2a+(n-1\left)d\right)=n^2$

so mean is = sum of series/total no of terms

$=n^2/n=n$