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Find the first 3 terms of the sequence whose [tex]\( n \)[/tex]th term is given by:

[tex]\[ A_n = 4^n \][/tex]

Sagot :

GinnyAnsweridn
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.
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