To find the first three terms of the sequence defined by the nth term [tex]\[ A(n) = 4^n \][/tex], we need to evaluate the function for [tex]\( n = 1 \)[/tex], [tex]\( n = 2 \)[/tex], and [tex]\( n = 3 \)[/tex].
1. First Term ([tex]\( A(1) \)[/tex]):
- Substitute [tex]\( n = 1 \)[/tex] into the sequence formula.
- [tex]\( A(1) = 4^1 \)[/tex]
- Calculate the value:
[tex]\[
4^1 = 4
\][/tex]
2. Second Term ([tex]\( A(2) \)[/tex]):
- Substitute [tex]\( n = 2 \)[/tex] into the sequence formula.
- [tex]\( A(2) = 4^2 \)[/tex]
- Calculate the value:
[tex]\[
4^2 = 16
\][/tex]
3. Third Term ([tex]\( A(3) \)[/tex]):
- Substitute [tex]\( n = 3 \)[/tex] into the sequence formula.
- [tex]\( A(3) = 4^3 \)[/tex]
- Calculate the value:
[tex]\[
4^3 = 64
\][/tex]
Therefore, the first three terms of the sequence are 4, 16, and 64.
