Question

what is the sum of the first 30 terms of the arithmetic sequence : -3,0,3,6...84

Answer 1

Answer:

$1,215$

Step-by-step explanation:

we have

$-3,0,3,6...84$

$a_1=-3\\a_2=0\\a_3=3\\a_4=6$

$a_2-a_1=0-(-3)=3$

$a_3-a_2=3-0=3$

$a_4-a_3=6-3=3$

so

The common difference d is 3

we know that

The rule to find the sum of the the first n terms of the arithmetic sequence is equal to

$S=\frac{n}{2} [2a_1+(n-1)d]$

where

d is the common difference

a_1 is the first term

we have

$d=3\\a_1=-3\\n=30$

substitute in the formula

$S=\frac{30}{2} [2(-3)+(30-1)3]$

$S=15[-6+87]$

$S=1,215$