Question

What is the sum of the first $10$ multiples of $6$?

Answer 1

Determine the sum of the first$10$ multiples of $6$.

First$10$ multiples of $6$ are $6,12,18\dots \dots ..60$

From the above sequence, we note that it is an A.P

$$\begin{gathered} \text{First term}=a=6 \\ \text{commom difference}=d=6 \end{gathered}$$

Use the formula to calculate the sum.

$$\begin{gathered} \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathit{S}}_{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}}{\mathbf{2}}\mathbf{[}\mathbf{}\mathbf{2}\mathbf{}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\mathbf{(}\mathbf{}\mathit{n}\mathbf{–}\mathbf{1}\mathbf{)}\mathbf{}\mathit{d}\mathbf{}\mathbf{]} \\ =\frac{10}{2}[2\times 6+(10-1)\times 6] \\ =5[12+54] \\ =5\times 66 \\ =330 \end{gathered}$$

Hence, the sum of the first$10$ multiples of $6$ is $330$