Answer :
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:
[tex]a_n=a_1+(n-1).r\\ \\ 99=3+3(n-1)\\ \\ 99-3=3n-3\\ \\ 3n=99\\ \\ n=33[/tex]
Calculating sum:
[tex]S_{33}=\frac{33(a_1+a_{33})}{2}\\ \\ S_{33}=\frac{33(3+99)}{2}=\frac{33*102}{2}=1683[/tex]
a1 = 3
an = 99
r = 3
Using the formula of general terms:
[tex]a_n=a_1+(n-1).r\\ \\ 99=3+3(n-1)\\ \\ 99-3=3n-3\\ \\ 3n=99\\ \\ n=33[/tex]
Calculating sum:
[tex]S_{33}=\frac{33(a_1+a_{33})}{2}\\ \\ S_{33}=\frac{33(3+99)}{2}=\frac{33*102}{2}=1683[/tex]
