Question

Find the sum of the multiples of 3 from 3 to 99 inclusive

Answer 1

Multiples of 3 from 3 to 99 inclusive is a Aritmetic Progression where:

a1 = 3 
an = 99
r = 3

Using the formula of general terms:

$a_n=a_1+(n-1).r\\ \\ 99=3+3(n-1)\\ \\ 99-3=3n-3\\ \\ 3n=99\\ \\ n=33$

Calculating sum:

$S_{33}=\frac{33(a_1+a_{33})}{2}\\ \\ S_{33}=\frac{33(3+99)}{2}=\frac{33*102}{2}=1683$