Question

Find $r$, given that $a_1=10$ and $a_{20}={10}^{-18}$

• A. $0.1$
• B. $0.01$
• C. $0.2$
• D. $0.03$

Answer 1

Answer: (A)

$0.1$

In a geometric series $a_n=a\cdot r^{n-1}$ where $a_1$ is the first term of the sequence, $r$ is the common ratio and $n$ is the number of the term to find.

Since the first term is $10$, therefore,

$a_{20}=10{\left(r\right)}^{20-1}=10{\left(r\right)}^{19}\Rightarrow {10}^{-18}=10r^{19}\Rightarrow r^{19}=\frac{{10}^{-18}}{10}\Rightarrow r^{19}={10}^{-18-1}\Rightarrow r^{19}={10}^{-19}\Rightarrow r={10}^{-1}\Rightarrow r=\frac{1}{10}$