# 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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#### Explanation:

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Mar 8, 2018

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#### Explanation:

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 $- \frac{3}{2}$.

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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