Question

Please help!
What is the tenth term of the geometric sequence that has a common ratio of 1/3 and 36 as its fifth term?
A: 4/27
B: 27/4
C: 4/81
D: 1/36

Answer 1

\(\bf \large {a_n=a_1\cdot r^{n-1}\qquad a_5=36\quad \textit{common ratio }\cfrac{1}{3}\qquad thus\\ \quad \\
a_5=a_1\cdot \left(\cfrac{1}{3}\right)^{5-1}\implies
36=a_1\cdot \left(\cfrac{1}{3}\right)^{4}}\)

find \(\bf a_1\) or the 1st term, keeping in mind that the 10th term is \(\bf \large a_{10}=a_1\cdot \left(\cfrac{1}{3}\right)^{10-1}\)