https://file.aiquickdraw.com/mathbot/file/1727267300569frtwruit.jpg

The sequence provided is defined as:

\[
a_n = 2(2^n)
\]

We are tasked with finding the first five terms, starting with \( n = 1 \).

Let's calculate the terms:

1. For \( n = 1 \):
\[
a_1 = 2(2^1) = 2 \times 2 = 4
\]

2. For \( n = 2 \):
\[
a_2 = 2(2^2) = 2 \times 4 = 8
\]

3. For \( n = 3 \):
\[
a_3 = 2(2^3) = 2 \times 8 = 16
\]

4. For \( n = 4 \):
\[
a_4 = 2(2^4) = 2 \times 16 = 32
\]

5. For \( n = 5 \):
\[
a_5 = 2(2^5) = 2 \times 32 = 64
\]

Thus, the first five terms of the sequence are:

\[
4, 8, 16, 32, 64
\]

Let me know if you'd like more details or have any questions!

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**Related questions:**
1. How would the sequence change if the base of the exponent were 3 instead of 2?
2. What is the general formula for the sum of the first \( n \) terms of this sequence?
3. How does this sequence relate to geometric progressions?
4. What happens if we change the multiplier from 2 to another constant?
5. How do we derive the \( n \)-th term for this type of exponential sequence?

**Tip:** In exponential sequences, each term grows rapidly due to the power function. Understanding how the exponent affects growth is key to analyzing such sequences.

Find the first five terms of the sequence defined by a_n = 2(2^n), starting with n = 1.

Learn how to find the first five terms of the sequence defined by a_n = 2(2^n), starting with n = 1. Explore key exponential concepts, suitable for Grades 7-9.

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