Answer :

The sum of 8 terms in sequence is 3.83.

What is sequence?

The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, but a sequence is an ordered group of elements in which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.

Here the given sequence is [tex]\frac{5}{6},\frac{25}{36},\frac{125}{216},\frac{625}{1296},\frac{3125}{7776},...[/tex]

Now common ratio r = [tex]\frac{a_2}{a_1}=\frac{25/36}{5/6}[/tex] = [tex]\frac{25}{36}\times\frac{6}{5} = \frac{5}{6}[/tex]

First term [tex]a_1=\frac{5}{6}[/tex]

Now using formula then,

=> [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex] where n=8 then,

=> [tex]S_8=\frac{\frac{5}{6}(1-\frac{5}{6}^8)}{1-\frac{5}{6}}[/tex]

=> [tex]S_8[/tex] = 3.83

Hence the sum of 8 terms in sequence is 3.83.

To learn more about sequence refer the below link

https://brainly.com/question/7882626

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Thanks for taking the time to read Find the sum of the first n terms using the formula a 1 r 1 r 5 25 125 625 6 36 216 1296 3125. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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