Bluecopper13
Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A 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]

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.