A geometric sequence is defined by the explicit formula $a_n = 5(-3)_(n-1)$ , what is the recursive formula for the nth term of this sequence?

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Answer 1 · 2016-09-07T07:56:50

The recursive formula is:

${(a_1=5),(a_{n+1}=-3a_n):}$

I assume the formula is: $a_n=5(-3)^{n-1}$ .

To calculate the recursive formula first we can calculate some terms of the sequence:

$a_1=5*(-3)^(1-1)=5*(-3)^0=5$

$a_2=5*(-3)^(2-1)=5*(-3)^1=-15$

$a_3=5*(-3)^(3-1)=5*(-3)^2=45$

From these calculations we see that the first term is $a_1=5$ and each other term comes from multiplying previous one by $-3$ .

This algorithm can be written as the recursive formula:

${(a_1=5),(a_{n+1}=-3a_n):}$

A geometric sequence is defined by the explicit formula a_n = 5(-3)_(n-1)a_n = 5(-3)_(n-1), what is the recursive formula for the nth term of this sequence?