The fifteenth term of the of the given sequence 5, -10, 20, -40, 80 is 81920.
A sequence of nom-zero numbers where each item after the first is found by multiplying the previous one by a fixed, non-zero number is called common ratio. It is represented by
[tex]a, ar^{2}, ar^{3} ,ar^{2}...[/tex]so on
where a is the first term
r is the common ratio.
nth term = [tex]ar^{n-1}[/tex]
According to the given question
We have
Geometric sequence is 5, -10, 20, -40, 80
first term, a =5
common ratio, r =[tex]\frac{-10}{5}[/tex] = -2
Therefore,
the fifteenth term of the sequence is given by
[tex]T_{15} =ar^{15-1}[/tex]
substitute, a = 5 and r = -2 in the above expression
[tex]T_{15} = 5(-2)^{14}[/tex]
[tex]T_{15} = 5(16384)[/tex]
[tex]T_{15} = 81920[/tex]
Hence, the fifteenth term of the sequence 5, -10, 20, -40, 80 is 81920.
Learn more about the geometric progression here:
https://brainly.com/question/4853032
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