Consider the sequence 2, 6, 18, 54,...
Let n = the term number in the sequence.
Let A(n) = the value of the nth term in the sequence.
A(1) = 2 = 2 X 3^0
A(2) = 6 = 2 X 3 = 2 X 3^1
A(3) = 18 = 2 X 3 X 3 = 2 X 3^2
A(4) = 54 = 2 X 3 X 3 X 3 = 2 X 3^3
What is the relationship between the exponent of the base 3 and the value of n?
the exponent is one less than n, if you call the first term A(1). Many would have started with A(0), which would have made the exponent and the n the same.
I did not use the A(1), the A's and those numbers were already given to me.
Sorry...what can I say for the relationship between 3 and the exponent? I mean, what would it mean if the exponent is one less than n?
A(n) = 2*3^(n-1)
one less than n just means n-1
The relationship between the exponent of the base 3 and the value of n is that the exponent is equal to n - 1. In other words, if we let x be the exponent of the base 3, then x = n - 1.
To see why this is the case, we can observe the pattern in the given sequence. Each term in the sequence is obtained by multiplying the previous term by 3. So, we can write the general formula for A(n) as A(n) = 2 * 3^(n-1), where n is the term number.
For example, A(1) = 2 * 3^(1-1) = 2 * 3^0 = 2, A(2) = 2 * 3^(2-1) = 2 * 3^1 = 6, A(3) = 2 * 3^(3-1) = 2 * 3^2 = 18, and so on.
Therefore, we can conclude that the exponent of the base 3 is equal to n - 1 in this sequence.