the nth term of a sequence is log(n +3) to base 2. what is the difference between the 13th term and the first term?
term(n) = log2(n+3)
term(13) = log2(16)
term(1) = log2(4)
difference = log216 - log24
= log2(16/4)
= log2 4
= 2
Well, that sounds like a logarithmically funny situation! Let's find the first and 13th terms of the sequence and see what the difference is.
To find the first term, we substitute n = 1 into the formula: log(1 + 3) to base 2. Logarithms are like hidden mathematician jokes, so we can laugh while calculating. log(1 + 3) is log(4), and to base 2, that's log₃₂(4). And since we all know that 2² is 4, the first term is 2.
Now, let's move on to the 13th term. Plugging n = 13 into the formula, we get log(13 + 3) to base 2, which simplifies to log(16), or log₃₂(16). Since 2⁴ is 16, the 13th term is 4.
Finally, we subtract the first term (2) from the 13th term (4) to find the difference. 4 - 2 = 2. So, the difference between the 13th term and the first term of the sequence is 2.
Hope that brought a logarithmic smile to your face!
That's not my question
To find the difference between the 13th term and the first term of the sequence, we need to find both terms separately and then subtract the first term from the 13th term.
Given that the nth term of the sequence is given by log(n+3) to base 2, we can substitute n=13 and n=1 to find the respective terms.
Calculating the 13th term:
13th term = log(13 + 3) to base 2
= log(16) to base 2
= log2(16)
Calculating the first term:
1st term = log(1 + 3) to base 2
= log(4) to base 2
= log2(4)
Now, we can find the difference between the 13th term and the first term:
Difference = 13th term - 1st term
= log2(16) - log2(4)
To subtract logarithms with the same base, we can divide inside the logarithm:
Difference = log2(16/4)
= log2(4)
= 2
Therefore, the difference between the 13th term and the first term is 2.
To find the difference between the 13th term and the first term of a sequence, you first need to find the value of the individual terms and then subtract the first term from the 13th term.
In the given sequence, the nth term is log(n+3) to the base 2. To find the value of the first term, substitute n = 1 into the formula:
1st term = log(1 + 3) to base 2
= log(4) to base 2
To simplify the expression, you can use the logarithmic identity logₐ(b^c) = c * logₐ(b):
1st term = log(4) to base 2
= log₂(4)
= log₂(2^2)
= 2
So, the value of the first term is 2.
Similarly, to find the value of the 13th term, substitute n = 13 into the formula:
13th term = log(13 + 3) to base 2
= log(16) to base 2
= log₂(16)
= log₂(2^4)
= 4
The value of the 13th term is 4.
Now, to find the difference between the 13th term and the first term, subtract the first term from the 13th term:
Difference = 13th term - 1st term
= 4 - 2
= 2
Therefore, the difference between the 13th term and the first term is 2.