Question

Find the sum of the first 10 multiples of 3.

Answer 1

Multiples of 3 are:
3, 6, 9, ...

They are in A.P. with
First term (a) = 3
Common difference (d) = 6 − 3 = 3

$$\begin{gathered} S_{10}=\frac{10}{2}\left[2a+\left(10-1\right)d\right] \\ =5\left[2a+9d\right] \\ =5\left[2\left(3\right)+9\left(3\right)\right] \\ =5\left[6+27\right] \\ =5\times 33 \\ =165 \end{gathered}$$

​Hence, the sum of the first 10 multiples of 3 is 165.