Bluecopper13
Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Find the sum of the geometric sequence −3, 15, −75, 375, ... when there are 9 terms and select the correct answer below. (2 points)


−976,563

976,563

1,464,843

976,562

Sagot :

Heather

Answer: −976,563

Step-by-step explanation:

    Since we have a negative constant of proportionality, the 9th term must be negative. This means our answer will be −976,563, however, I will still show the steps to get there mathematically.

    We will find the sum of the geometric sequence to 9 terms with the following formula. Here, a is the first term (-3), r is the constant of proportionality (15/-3=-5), and n is the number of terms (9).

         [tex]\displaystyle S_n=\frac{a(r^n-1)}{r-1}[/tex]

         [tex]\displaystyle S_n=\frac{-3((-5)^9-1)}{-5-1}[/tex]

         [tex]\displaystyle S_n=\frac{-3(-1,953,125-1)}{-5-1}[/tex]

         [tex]\displaystyle S_n=\frac{-3(-1,953,126)}{-6}[/tex]

         [tex]\displaystyle S_n=\frac{5,859,378}{-6}[/tex]

         [tex]\displaystyle S_n=-976,563[/tex]

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.