Question

Calculate the sum of even numbers between 100 and 150 which are divisible by 13.

• A. $494$
• B. $410$
• C. $420$
• D. $430$

Answer 1

The correct option is A $494$

The even numbers between $100$ and $150$ which are divisible by $13$ are $104,117,............143$

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 $=104$

$d=$ common difference of A.P. $=13$

$T_n=$ Last term $=143$

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

$143=104+(n-1)13$

$143=104+13n-13$

$143-104+13=13n$

$52=13n$

$n=4$

Apply the given data in the formula (1),

$S_4=\frac{4}{2}[2\times 104+(4-1\left)13\right]$

$=2[208+(3\left)13\right]$

$=2[208+39]$

$=2\left[247\right]$

$=494$

So, the sum of even numbers between $100$ and $150$ which are divisible by $13$ is $494$.