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)=(33(a_1+a_(33)))/(2)\\ \\ S_(33)=(33(3+99))/(2)=(33*102)/(2)=1683`