Question

Which term of the geometric sequence is 1/8 if the first term is 4 and common ratio ½

Answer 1

Solution.

We have geometric sequence, where $b_1=4,$ $r=\frac{1}{2}$ and $b_n=\frac{1}{8}.$ Find $n.$

By the formula $b_n=b_1r^{n-1}$ we will have $\frac{1}{8}=4•(\frac{1}{2})^{n-1}.$

Solve this equation

$$\frac{1}{32}=(\frac{1}{2})^{n-1},\newline (\frac{1}{2})^5=(\frac{1}{2})^{n-1},\newline 5=n-1,\newline n=6.$$

Answer. The sixth term of the geometric sequence is $\frac{1}{8}.$