Question

The sum of all natural numbers between $100$ and $1000$ which are multiple of $5$ is

• A. $98,450$
• B. $96,450$
• C. $97,450$
• D. $95,450$

Answer 1

The correct option is A $98,450$

We know,

$n^{th}$ term $a_n=a+(n-1)d$

$a=$ First term

$d=$ Common difference

$n=$ number of terms

$t_n=n^{th}$ term

Here $a=105,d=5$ numbers form an A.P.

$a+(n-1)d=995$

$105+(n-1)5=995$

$(n-1)5=995-105=890$

$n-1=178$

$n=179$

We know, Sum of n terms

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

$S_n=\frac{179}{2}\left[2\right(105)+(179-1\left)5\right]$

$=\frac{179}{2}\left[2\right(105)+178\times 5]$

$=179(105+89\times 5)$

$=179\left(550\right)$

$=98450$.