3 years ago

Could use help on this one! Will give Brainliest to the correct answer and thanks

Mathematics

2 answers:

mariarad [96]3 years ago

8 0

The answer I got was B.

Gnesinka [82]3 years ago

4 0

D. Is the answer if im wrong then you don't have to thank me

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If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16 then what is the fourteenth term?

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<h3>Given</h3>

A geometric sequence such that ...

$a_2=-2\quad\text{and}\quad a_5=16$

$a_{14}$

<h3>Solution</h3>

We can use the ratio of the given terms to find the common ratio of the sequence, then use that to find the desired term from one of the given terms. We don't actually need the common ratio (-2). All we need is its cube (-8).

$a_2=a_1r^{(2-1)}=a_1r^1\\a_5=a_1r^{(5-1)}=a_1r^4\\a_{14}=a_1r^{(14-1)}=a_1r^13=a_5r^9\\\\\dfrac{a_5}{a_2}=\dfrac{a_1r^4}{a_1r^1}=r^3=\dfrac{16}{-2}=-8\\\\r^9=\left(r^3\right)^3=(-8)^3=-512\\a_{14}=a_5(-512)\\\\a_{14}=-8192$

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