ANSWER
[tex]\text{The 5th term of the sequence is s}^{\frac{8}{7}}[/tex]
STEP-BY-STEP EXPLANATION
Given the sequence below
[tex]1,s^{\frac{2}{7}},s^{\frac{4}{7}},\text{ }s^{\frac{6}{7}}[/tex]
The common ratio of the sequence is given below as
[tex]s^{\frac{2}{7}}[/tex]
The general formula for finding the nth term of a geometric sequence is
[tex]a_n=ar^{n\text{ - 1}}[/tex]
Where,
0. a = first term
,
1. r = common ratio
,
2. n = number of terms
To find the 5th term of the geometric, then n = 5
[tex]\begin{gathered} a\text{ = 1} \\ n\text{ = 5} \\ r=s^{\frac{2}{7}} \\ a_5\text{ = 1 }\cdot S^{\frac{2(5\text{ - 1)}}{7}} \\ a_5=s^{\frac{2(4)}{7}} \\ a_5=s^{\frac{8}{7}} \end{gathered}[/tex]
NB: When inputting your answer in the box, use the small letter 's' and not the capital letter S
