Question

What is the sum of the geometric series?

Answer 1

Answer:

40

Step-by-step explanation:

The given geometric series is:

$\sum_{n=1}^4(-2)(-3)^{n-1}$.

When n=1, $a_1=(-2)(-3)^{1-1}$, $\implies a_1=(-2)(-3)^{0}=-2$

When n=2, $a_2=(-2)(-3)^{2-1}$, $\implies a_2=(-2)(-3)^{1}=6$

When n=3, $a_3=(-2)(-3)^{3-1}$, $\implies a_3=(-2)(-3)^{2}=-18$

When n=4, $a_4=(-2)(-3)^{4-1}$, $\implies a_4=(-2)(-3)^{3}=54$

The sum of the given series is:

-2+6-18+54=40