write an equation to decribe the sequence below. use n to represent the position of a term in the sequence, where n=1 for the first term
1,4,16,...
write your answer using decimals and integers
The sequence is an example of a geometric sequence, where each term is obtained by multiplying the previous term by a constant value, in this case, 4.
To write an equation for this sequence, we need to find the common ratio (r) between consecutive terms.
The first term is 1, the second term is 4, and the third term is 16.
To move from the first term to the second term, we multiply by 4: 1 * 4 = 4.
To move from the second term to the third term, we multiply by 4 again: 4 * 4 = 16.
This shows that the common ratio between consecutive terms is 4.
Therefore, the equation to describe this sequence using n as the position of a term is:
a(n) = 1 * 4^(n-1), where a(n) represents the value of the nth term.
For example, if we plug in n = 1:
a(1) = 1 * 4^(1-1) = 1 * 4^0 = 1 * 1 = 1.
If we plug in n = 2:
a(2) = 1 * 4^(2-1) = 1 * 4^1 = 1 * 4 = 4.
Similarly, if we plug in n = 3:
a(3) = 1 * 4^(3-1) = 1 * 4^2 = 1 * 16 = 16.
Therefore, the equation a(n) = 1 * 4^(n-1) describes the given sequence.