Answer:
-130
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
a(n) = a(1)*r*(n - 1), where r is the common ratio, a(1) is the first term and n is the index.
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Here r = -2 and the first term is 5. Thus,
a(14) = 5(14 - 1)(-2) = 5(13)(-2) = -130
14th term of the geometric sequence is -40960.
"A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3."
We have
Geometric sequence
5, -10, 20 .............
[tex]a_{n} = a_{1}[/tex]×[tex]r^{n-1}[/tex]
⇒[tex]a_{14}[/tex] = [tex]5[/tex]×[tex](-2)^{14-1}[/tex]
⇒[tex]a_{14}[/tex] = [tex]5[/tex]×[tex](-2)^{13}[/tex]
⇒[tex]a_{14}[/tex] = [tex]-40960[/tex]
Hence, 14th term of the geometric sequence is -40960.
Learn more about geometric sequence here
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