Question

Name the next four terms of each arithmetic sequence.
5,9,13, ...
(show steps)

Answer 1

To find the next four terms of the arithmetic sequence 5, 9, 13, ..., we first need to determine the common difference.

1. **Identifying the Common Difference:**
- The first term is \( a_1 = 5 \).
- The second term is \( a_2 = 9 \).
- The third term is \( a_3 = 13 \).

To find the common difference \( d \):
\[
d = a_2 - a_1 = 9 - 5 = 4
\]
\[
d = a_3 - a_2 = 13 - 9 = 4
\]
The common difference \( d \) is \( 4 \).

2. **Finding the Next Four Terms:**
Now we can find the next terms in the sequence by adding the common difference \( d \) to the last known term.

- Fourth term (\( a_4 \)):
\[
a_4 = a_3 + d = 13 + 4 = 17
\]

- Fifth term (\( a_5 \)):
\[
a_5 = a_4 + d = 17 + 4 = 21
\]

- Sixth term (\( a_6 \)):
\[
a_6 = a_5 + d = 21 + 4 = 25
\]

- Seventh term (\( a_7 \)):
\[
a_7 = a_6 + d = 25 + 4 = 29
\]

3. **Final Listing of Terms:**
The next four terms in the sequence are:
\[
17, 21, 25, 29
\]

So the final answer is: **17, 21, 25, 29.**