Question
Find the 13 th term of the geometric sequence
Answer Attempt tout of 3

Ask by Nguyen Watkins. in the United States

Mar 16,2025

Question

Question Find the 13 th term of the geometric sequence $$ 5,10,20, \ldots $$ Answer Attempt tout of 3 $$ \square $$

UpStudy AI · Accepted Answer

To find the 13th term of the geometric sequence $$ 5, 10, 20, \ldots $$, we first need to identify the first term and the common ratio.

1. **Identify the first term ($$ a $$)**:
   - The first term $$ a = 5 $$.

2. **Identify the common ratio ($$ r $$)**:
   - The common ratio can be found by dividing the second term by the first term:
   $$
   r = \frac{10}{5} = 2
   $$

3. **Use the formula for the $$ n $$-th term of a geometric sequence**:
   The formula for the $$ n $$-th term ($$ T_n $$) of a geometric sequence is given by:
   $$
   T_n = a \cdot r^{(n-1)}
   $$
   where $$ a $$ is the first term, $$ r $$ is the common ratio, and $$ n $$ is the term number.

4. **Substitute the values to find the 13th term**:
   - Here, $$ n = 13 $$:
   $$
   T_{13} = 5 \cdot 2^{(13-1)} = 5 \cdot 2^{12}
   $$

Now, we will calculate $$ 2^{12} $$ and then multiply by 5.

Let's calculate $$ 2^{12} $$ first.

$$
2^{12} = 4096
$$

Now, substituting back into the equation for $$ T_{13} $$:

$$
T_{13} = 5 \cdot 4096 = 20480
$$

Thus, the 13th term of the geometric sequence is $$ 20480 $$.
The 13th term of the geometric sequence is 20,480.

Question
Find the 13 th term of the geometric sequence
Answer Attempt tout of 3

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Pre Algebra Questions

Question Find the 13 th term of the geometric sequence Answer Attempt tout of 3