Question

The first term of a geometric sequence is $10$ and the fifth term is $160$. What is the common ratio?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Let the first term be $a$ and the common ratio be $r$
Since, first term $a=10$
Use the formula for the nth term: $a_n=a{r}^{n-1}$
The fifth term $=$ $160=10r^{5-1}$
$\Rightarrow 160=10r^4$
$\Rightarrow 16=r^4$

Taking fourth root, we get
$r=2$