How do you write the first five terms of the geometric sequence #a_1=6, a_(k+1)=-3/2a_k# and determine the common ratio and write the nth term of the sequence as a function of n?

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Mar 8, 2018

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A geometric sequence is defined as: an ordered sequence of number such that each term is calculated multipliying the prior term by a constant number called ratio. In mathematical terms

#a_(k+1)=r·a_k# or if you want #a_k=r·a_(k-1)#

In our case #a_(k+1)=-3/2·a_k#. So, the ratio is #-3/2#.

Lets calculate:

#a_1=6#
#a_2=-3/2·6=-9#
#a_3=-3/2·(-9)=+27/2#
#a_4=-3/2·27/2=-81/4#
#a_5=-3/2·(-81/4)=+243/8#

The general term is given by #a_n=a_1·r^(n-1)#...in our case

#a_n=6·(-3/2)^(n-1)#

Each term with a odd position will be positive and each term in a even postion will be negative (oscillating)

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