Question

What is the sum of 12 odd numbers $1,3,5,7,\mathrm{9.....}?$

• A. $12$
• B. $144$
• C. $141$
• D. $124$

Answer 1

Answer: (B)

$144$

First term of the given arithmetic series $=1$
Second term of the given arithmetic series $=3$
Third term of the given arithmetic series $=5$
Fourth term of the given arithmetic series $=7$
Now, Second term - First term $=3-1=2$
Third term - Second term $=5-3=2$
Therefore, common difference of the given arithmetic series is $2.$
The number of terms of the given $A.P.$ series $\left(n\right)=12$
We know that the sum of first n terms of the Arithmetic Progress, whose first term$=a$ and common difference$=d$ is
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$S_{12}=\frac{12}{2}[2\times 1+(12-1\left)2\right]$

$S_{12}=6[2+22]$

$S_{12}=144$