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Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence,where n = 1 for the first term.

5, -3 , 9/5 , ...

Write your answer using proper fractions, improper fractions, and integers.

an = [tex]( )^{n-1}[/tex]n - 1

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ANSWER

The required equation is:

[tex]a_n=5( - \frac{3}{5} )^{n-1}[/tex]

EXPLANATION

The given sequence is

[tex]5, -3 , \frac{9}{5} [/tex]

The first term of the sequence is ;

[tex]a_1=5[/tex]

The common ratio is the subsequent term previous term of any two consecutive terms. This implies that;

[tex]r = \frac{ - 3}{5} [/tex]

The nth term of the sequence is

[tex]a_n=a_1(r)^{n-1}[/tex]

We substitute the terms to obtain;

[tex]a_n=5( - \frac{3}{5} )^{n-1}[/tex]

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