Question

Calculate the sum of whole numbers between 0 and 79 which are divisible by 11.

• A. $300$
• B. $310$
• C. $308$
• D. $320$

Answer 1

Answer: (C)

$308$

The numbers between $0$ and $79$ which are divisible by $11$ are $11,22,33,44,......77$.

The sum of first $n$ terms of arithmetic series formula can be written as,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ ............ (1)

Where $n=$ number of terms = ?

$a=$ first odd number $=11$

$d=$ common difference of A.P. $=11$

$T_n=$ Last term $=77$

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

$77=11+(n-1)11$

$77=11+11n-11$

$77-11+11=11n$

$77=11n$

$\Rightarrow n=7$

Apply the given data in the formula $\left(1\right)$, we get

$S_7=\frac{7}{2}[2\times 11+(7-1\left)11\right]$

$=3.5[22+(6\left)11\right]$

$=3.5[22+66]$

$=3.5\left[88\right]$

$=308$

So, the sum of whole numbers between $0$ and $79$ which are divisible by $11$ is $308$.