Question

What is the sum of the arithmetic sequence 3,9,15...if there are 24 terms?

Answer 1

$a_1=3;\ a_2=9;\ a_3=15;\ ...\\\\d=a_2-a_1\to d=9-3=6$

The formula of the sum of the arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}cdot n$

Substitute:

$a_1=3;\ d=6;\ n=24\\\\S_{24}=\dfrac{2\cdot3+(24-1)\cdot6}{2}\cdot24=(6+23\cdot6)\cdot12=(6+138)\cdot12=144\cdot12=1,728$

Answer: 1,728.