Question

Find the sum of the geometric sequence 3, 15, 75, 375, … when there are 9 terms and select the correct answer below.

a. -976,563
b. 976,563
c. 1,464,843
d. 976,562

Answer 1

Answer: -976,563 PLEASE READ DESCRIPTION

Explanation:

My question had the same exact numbers but some of them were negative! Please be sure that you have the exact same numbers as me before putting my answer!!

"Find the sum of the geometric sequence −3, 15, −75, 375, ... when there are 9 terms and select the correct answer below"

-3 X -5 = 15 X -5 = -75 X -5 = 375.

Ratio = -5

Use the formula
`s_(n) = (a_(1 - a_1 (r)^(n) ))/(1 - r)`.

Our
`a_1` (first term) = -3, r (ratio)= -5, and n (number of terms) = 9. Knowing this, plug them into the equation.

`s_9 = (-3 - (-3)(-5)^9)/(1-(-5))`.

First, simplify the exponent. -5 to the ninth power = -1,953,125. Multiply this by the nearest number in exponents (-3). -1,953,125 X -3 = 5,859,375. Continue simplifying your numerator. -3 - (5,859,375) = -5,859,378. Now, simplify your denominator. 1 - (-5) = 6.

Divide.

`s_9 = (-5,859,372)/(6)` = -976,563

I tried to make sure there weren't any typos, but please comment if there's something wrong!

Answer 2

c. 1,464,843

Explanation:

The sum of n terms of a geometric sequence with first term a1 and common ratio r is given by ...

sn = a1(r^n -1)/(r -1)

Filling in the values a1=3, r=5, n=9, we get ...

s9 = 3(5^9 -1)/(5 -1) = 1,464,843