How do you find nth term rule for #a_1=1/4# and #a_3=6#?

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Answer 1 · 2016-08-02T18:30:25

The formula for the #n#th term is one of the following:

#a_n = 1/4 (2sqrt(6))^(n-1)#

#a_n = 1/4 (-2sqrt(6))^(n-1)#

Assuming this is a geometric sequence...

The general term of a geometric sequence is given by the formula:

#a_n = ar^(n-1)#

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

So we have #a = a_1 = 1/4# and we find:

#r^2 = (ar^2)/(ar^0) = a_3/a_1 = 6/(1/4) = 24#

So:

#r = +-sqrt(24) = +-2sqrt(6)#

So the formula for the #n#th term is one of the following:

#a_n = 1/4 (2sqrt(6))^(n-1)#

#a_n = 1/4 (-2sqrt(6))^(n-1)#