The nth term of a sequence is log2(n+3) what is the difference between the 13th and the 1st term
using base 2 logs,
log16 - log4 = 4-2 = 2
Ah, calculating the difference between the 13th and 1st term of a sequence? Well, that's a logarithmic adventure! Let's dive in and have some fun with numbers!
To find the 13th term, we substitute n = 13 into the sequence expression: log2(13 + 3) = log2(16) = 4.
To find the 1st term, we substitute n = 1 into the sequence expression: log2(1 + 3) = log2(4) = 2.
Now, let's subtract the 1st term from the 13th term: 4 - 2 = 2.
Therefore, the difference between the 13th and 1st term is 2. Voila!
To find the difference between the 13th term and the 1st term of a sequence, we need to substitute the values of 13 and 1 into the given expression and then calculate the difference.
Let's find the 13th term first:
nth term = log2(n+3)
13th term = log2(13+3) = log2(16)
Now, let's find the 1st term:
nth term = log2(n+3)
1st term = log2(1+3) = log2(4)
Now, we can calculate the difference between the 13th and 1st terms:
Difference = 13th term - 1st term
= log2(16) - log2(4)
To simplify this, we can use the logarithmic property that states: loga(b) - loga(c) = loga(b/c)
Therefore:
Difference = log2(16) - log2(4)
= log2(16/4)
= log2(4)
= 2
So, the difference between the 13th and the 1st term is 2.
To find the difference between the 13th and 1st term of a sequence, we need to substitute the values of n into the given expression for each term and then subtract the 1st term from the 13th term.
Given that the nth term of the sequence is log2(n+3), we can substitute n = 13 and n = 1 to find the corresponding terms.
The 13th term:
T(13) = log2(13+3)
T(13) = log2(16)
T(13) = 4
The 1st term:
T(1) = log2(1+3)
T(1) = log2(4)
T(1) = 2
Now, we can calculate the difference between the 13th and 1st term:
Difference = T(13) - T(1)
Difference = 4 - 2
Difference = 2
Therefore, the difference between the 13th and 1st term of the sequence is 2.