Question

What is the sum of the geometric sequence -4, 24, -144, ... if there are 7 terms?

Answer 1

$a_1=-4;\ a_2=24;\ a_3=-144;\ ...\\\\r=\dfrac{a_2}{a_1}\\\\r=\dfrac{24}{-4}=-6$

The formula of the sum of a geometric sequence:

$S_n=\dfrac{a_1(1-r^n)}{1-r}$

We have:

$a_1=-4;\ r=-6;\ n=7$

substitute:

$S_7=\dfrac{-4(1-(-6)^7)}{1-(-6)}=\dfrac{-4(1-(-279,936))}{1+6}=\dfrac{-4(1+279,936)}{7}\\\\=\dfrac{-4\cdot279,937}{7}=-159,964$

Answer: A: -159,964