What is the fifteenth term of the sequence 5,-10,20,-40,80?

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What is the fifteenth term of the sequence 5,-10,20,-40,80?

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Answer 1 · 2016-02-26T01:55:55

$a_15=81920$

Explanation:

from the given set of numbers 5,-10,20,-40,80...it appears like Geometric Sequence and with first term $a_1=5$ and the common ratio $r=80/(-40)=(-40)/20=20/(-10)=(-10)/5=-2$

$r=-2$

the formula to find the $nth$ term in Geometric Progression is

$a_n=a_1*r^(n-1)$

Use now $a_1=5$ and $r=-2$ and $n=15$ in the formula

$a_n=a_1*r^(n-1)$

$a_15=5*(-2)^(15-1)$

$a_15=5*(-2)^(14)$

$a_15=5*16384$

$a_15=81920" " "$ the 15th term

A long check helps after all there are only 15 numbers

5, -10, 20, -40, 80, -160, 320, -640, 1280, -2560, 5120, -10240, 20480, -40960, 81920

God bless....I hope the explanation is useful...

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What is the fifteenth term of the sequence 5,-10,20,-40,80?

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