Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
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 service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
