The sequence is defined by the formula:

$a_n = 2(4)^n$

where $n$ represents the position of a term in the sequence.

Let's calculate the first five terms by substituting $n = 1, 2, 3, 4, 5$ into the formula:

1. For $n = 1$: $a_1 = 2(4)^1 = 2 \times 4 = 8$

2. For $n = 2$: $a_2 = 2(4)^2 = 2 \times 16 = 32$

3. For $n = 3$: $a_3 = 2(4)^3 = 2 \times 64 = 128$

4. For $n = 4$: $a_4 = 2(4)^4 = 2 \times 256 = 512$

5. For $n = 5$: $a_5 = 2(4)^5 = 2 \times 1024 = 2048$

Thus, the first five terms of the sequence are:

$8, 32, 128, 512, 2048$

Would you like more details or have any further questions on this?

Here are 5 related questions to explore:

1. How does the growth of this sequence compare to other types (e.g., linear or quadratic)?
2. What happens to the terms of the sequence as $n$ increases beyond 5?
3. Can you find the 10th term of this sequence?
4. How would the sequence change if the formula was $a_n = 3(4)^n$?
5. How would the sequence change if the formula was $a_n = 2(3)^n$?

Tip: In exponential sequences, the base (in this case, 4) dictates how quickly the values grow as $n$ increases.