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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