Answer:
[tex]a_{14}=-40960[/tex]
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
Given sequence:
First term
[tex]a=5[/tex]
Common ratio
To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{-10}{5}=-2[/tex]
Substitute the found values of a and r into the formula to create an equation for the nth term:
[tex]\implies a_n=5(-2)^{n-1}[/tex]
To find the 14th term, substitute n = 14 into the found equation:
[tex]\implies a_{14}=5(-2)^{14-1}[/tex]
[tex]\implies a_{14}=5(-2)^{13}[/tex]
[tex]\implies a_{14}=5(-8192)[/tex]
[tex]\implies a_{14}=-40960[/tex]
Therefore, the 14th term of the given geometric sequence is -40960.
Learn more about geometric sequences here:
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