How do you write a rule for the nth term of the geometric term given the two terms $a_1=1, a_3=9$ ?

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Answer 1 · 2017-05-21T18:21:45

There are two possible common ratios and corresponding sequences, given by the formula:

$a_n = 3^(n-1)" "$ or $" "a_n = (-3)^(n-1)$

The general formula for a term of a geometric sequence is:

$a_n = ar^(n-1)$

where $a$ is the initial term and $r$ the common ratio.

In our example, we find:

$9 = a_3/a_1 = (ar^2)/a = r^2$

Hence $r = +-3$ , giving two possible sequences.

The rule for the n $th$ term of this sequence can be written:

$a_n = 3^(n-1)$

or:

$a_n = (-3)^(n-1)$

How do you write a rule for the nth term of the geometric term given the two terms a_1=1, a_3=9a_1=1, a_3=9?