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)#