Is it possible for the sequence t(n)=5*2n(n is superscript) to have a term with the value of 200?
To determine if the sequence t(n) = 5 * 2^n can have a term with the value of 200, we need to find the value of n that satisfies the equation t(n) = 200.
To do this, we set up the equation:
5 * 2^n = 200
Dividing both sides of the equation by 5:
2^n = 40
To solve for n, we can take the logarithm of both sides of the equation. Let's take the base-2 logarithm (logarithm with base 2) of both sides:
log₂(2^n) = log₂(40)
Using the property of logarithms that states logₐ(b^c) = c * logₐ(b):
n * log₂(2) = log₂(40)
Since log₂(2) is equal to 1:
n = log₂(40)
Using a calculator or a logarithm table, we can find the approximate value of log₂(40), which is approximately 5.32.
Therefore, the sequence t(n) = 5 * 2^n does not have an integer value of n that satisfies t(n) = 200.