Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Using geometric sequence concepts, it is found that the sum of the first 10 terms is of 4068.6.
What is a geometric sequence?
- A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
- In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{a_1(q^n-1)}{q - 1}[/tex]
In this problem, the sequence is:
[tex]\frac{16}{25}, \frac{8}{5}, 4, 10,...[/tex]
Hence:
[tex]a_1 = \frac{16}{25}, q = \frac{10}{4} = 2.5[/tex]
Then, the sum of the first 10 terms is:
[tex]S_{10} = \frac{\frac{16}{25}(2.5^{10}-1)}{2.5 - 1} = 4068.6[/tex]
You can learn more about geometric sequence concepts at https://brainly.com/question/11847927
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
