To find the nth term of the sequence 4, 16, 64, 256, we first need to observe the pattern in the sequence. At first glance, we can notice that each term appears to be a power of 4:
- The first term is 4, which is equal to 41
- The second term is 16, equal to 42
- The third term is 64, equal to 43
- The fourth term is 256, equal to 44
This observation leads us to conclude that the nth term can be described by the equation:
T(n) = 4n
In this formula, T(n) represents the nth term of the sequence and n is the term’s index, starting from 1. Therefore:
- For n = 1, T(1) = 41 = 4
- For n = 2, T(2) = 42 = 16
- For n = 3, T(3) = 43 = 64
- For n = 4, T(4) = 44 = 256
Hence, the general formula for the nth term of the sequence 4, 16, 64, 256 is:
T(n) = 4n
This exponential function correctly generates each term in the sequence based on the value of n.