Question

What is the tenth term of the geometric sequence that has a common ratio of 1/3 and 36 as its fifth term?

a. 4/7
b. 27/4
c. 4/81
d. 1/36

Answer 1

To find any term
of a geometric sequence:

where a1 is the first term of the sequence,
r is the common ratio, n is the number of the term to find.

a5 = a1 * r^4;
36 = a1 * (1/3)^4;
a1 = 36 * 81;
a1 = 2916;

a10 = a1 * r^9;
a10 = 2916 * (1/3)^9;
a10 = 2916/13122;
a10 = 36/243;

Finally, a10 = 4/27;