Question

The sum of the given series $1+3+5+7+9+......+53$ is $729$.

• A. True
• B. False

Answer 1

The correct option is A True

We have,

$1+3+5+7+9+......+53$

$a=1,d=2,l=53$

We know that

$l=a+(n-1)d$

$53=1+(n-1)\times 2$

$n=27$

We know that

$S_{27}=\frac{27}{2}[2+(27-1)\times 2]$

$S_{27}=\frac{27}{2}[2+26\times 2]$

$S_{27}=\frac{27}{2}[2+52]$

$S_{27}=\frac{27}{2}\left[54\right]$

$S_{27}=729$

Hence, this is the answer.