How to find geometric sequence

Finding the nth Term of a Geometric Sequence

Given a geometric sequence with the first term a1 and the common ratio r , the nth (or general) term is given by
an=a1rn1 .

Example 1:

Find the 6th term in the geometric sequence 3,12,48,... .

a1=3,  r=123=4a6=3461=345=3072

Example 2:

Find the 7th term for the geometric sequence in which a2=24 and a5=3 .

Substitute 24 for a2 and 3 for a5 in the formula

an=a1rn1 .

a2=a1r2124=a1ra5=a1r51    3=a1r4

Solve the firstequation for a1 : a1=24r

Substitute this expression for a1 in the second equation and solve for r .


Substitute for r in the first equation and solve for a1 .


Now use the formula to find a7 .


See also: sigma notation of a series and nth term of a arithmetic sequence