Question

The sum of the integers from $1$ to $100$ which are divisible by $3$ and $5$, is

• A. $2317$
• B. $2632$
• C. $315$
• D. $2489$

Answer 1

The correct option is C

$315$

Explanation for the correct option:

Step 1: Form the required AP

LCM of $3$ and $5$$=15$ why did you calculate the LCM? explain

So, the terms divisible by $15$ which lie between $1$ to $100$ are part of A.P. how? explain

A.P.$=15,30,45,......,90$

Step 2: Find the sum of the AP

A.P.$=15,30,45,......,90$

$$\begin{gathered} a=15 \\ d=15 \\ {a}_n=a+(n-1)d \\ \Rightarrow 90=15+(n-1)15 \\ \Rightarrow n=6 \end{gathered}$$ what is a, d an and n? define.

Sum of the A.P, $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$

$$\begin{gathered} \Rightarrow S_6=\frac{6}{2}\left(2\right(15)+(6-1\left)15\right) \\ \Rightarrow S_6=3(30+75) \\ \Rightarrow S_6=315 \end{gathered}$$

Hence, the correct option is C.