To find the common ratio $r$ in a geometric sequence, we can use the formula for the $n$-th term of a geometric sequence:

$a_n = a_1 \times r^{n-1}$

where:

• $a_n$ is the $n$-th term,
• $a_1$ is the first term,
• $r$ is the common ratio,
• $n$ is the term number.

Given:

• The first term $a_1 = 10$,
• The fifth term $a_5 = 160$,
• $n = 5$.

We substitute these into the formula for the fifth term:

$160 = 10 \times r^{5-1}$

Simplify the exponent:

$160 = 10 \times r^4$

Next, solve for $r^4$ by dividing both sides by 10:

$r^4 = \frac{160}{10} = 16$

To find $r$, take the fourth root of both sides:

$r = \sqrt[4]{16} = 2$

Therefore, the common ratio is $r = 2$.

The correct answer is D. The common ratio in the sequence is 2.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How do you find the nth term of a geometric sequence?
2. What is the sum of the first $n$ terms in a geometric sequence?
3. How does the common ratio affect the growth of a geometric sequence?
4. Can the common ratio in a geometric sequence be negative? What would that look like?
5. How do geometric sequences differ from arithmetic sequences?

Tip: Always check if the common ratio is consistent by verifying it with another term in the sequence!