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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?

 Jul 1, 2020
 #1
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We use the equation a+d(n-1), where a is the first term and d is the common difference, and n is the nth term. 

 

We form two equations: a+d(1)=-2 and a+d(4)=16. We have a system of equations and solve.

 

a+d=-2

a+4d=16

 

-3d=-18

d=6, a=-8

 

So the fourteenth term is -8+6(14-1)=-8+6(13)=-8+78=70.

 Jul 1, 2020
 #2
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Thank you!

AnimalMaster  Jul 1, 2020

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