Question

What is the sum of all integers between $50$ and $350$ which have $1$ as the units digit?

• A. $5880$
• B. $5985$
• C. $6230$
• D. $6800$

Answer 1

The correct option is A $5880$

The sequence $51+61+\mathrm{71...}+341$ is an arithmetic progression.

$\Rightarrow$ To find the sum of n terms of an AP we use the formula.

$\Rightarrow$ Here, $n=30,a=51$ and $d=10$.

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

$\therefore$ $S_n=\frac{30}{2}[2\times 51+(30-1\left)10\right]$

$\therefore$ $S_n=15[102+290]$

$\therefore$ $S_n=15\times 392$

$\therefore$ $S_n=5880$