Question

Find the sum of all positive integers, from $5$ to $1555$ inclusive, that are divisible by $5$

• A. 242489
• B. 242580
• C. 242420
• D. 252420

Answer 1

Answer: (B)

242580

The first few terms of a sequence of positive integers divisible by $5$ is given by

$5,10,15,...$

The above sequence has a first term equal to $5$ and a common difference $d=5$. We need to know the rank of the term $1555$. We use the formula for the $nth$ term as follows

$1555=a_1+(n-1)d$

Substitute $a_1$ and $d$ by their values

$1555=5+5(n-1)$

Solve for $n$ to obtain

$n=311$

We now know that 1555 is the $311th$ term, we can use the formula for the sum as follows

$S_{311}=\frac{311(5+1555)}{2}=242580$