Question

What is the sum of first $100$ multiples of $12$?

• A. $60600$
• B. $61200$
• C. $62900$
• D. $60500$

Answer 1

The correct option is A $60600$

Frist $100$ multiples of $12$ will be,

$12,24,36,\dots$

So, we can conclude that the multiples of $12$ form an arithmetic progression whose first term is $12$ and the common difference is $12.$

The sum of first $n$ terms of an arithmetic series whose first term is $a$ and common difference is $d$ can be written as,
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

So, by using above formula,

$S_{100}=\frac{100}{2}[2\times 12+(100-1\left)12\right]$
$=50[24+(99\left)12\right]$
$=50[24+1188]$
$=50\times 1212$
$=60,600$

So, the sum of the first $100$ multiples of $12$ is $60600.$