Write an explicit formula for the sequence one-half, three-sevenths, one-third, five-nineteenths, three-fourteenths, ... Then find a14. (1 point)
an = an – 1 – n minus one over seven n; fifteeen over one hundred nintey nine
an = a sub n plus one over n squared plus three ; fifteen over one hundred nintey nine
an = n plus one over n squared plus three ; fifteen over one hundred nintey nine
an = n over n cubed minus one ; fifteen over one hundred nintey nine
what's with all the words? We have perfectly good digit keys...
1/2, 3/7, 1/3, 5/19, 3/14, ...
Looks pretty random, but we know we are after something we can easily relate to n. What if we get the denominators steadily increasing? Rewrite the sequence as
2/4, 3/7, 4/12, 5/19, 6/28
So, now it's easy to see that
an = (n+1)/(n^2+3)
a11 = 12/124 = 3/31
Dunno quite what to make of all the verbage below that. Try using some symbols and asking a question.
Hahaha! Oh Steve you crack me up with all that verbage and question asking. Anyways the question said to find a14, NOT a11. a14 = 15/199. So out of the wordy answer choices Paige gave, the answers C.
To write an explicit formula for the sequence, we need to find the pattern in the given terms.
Looking at the sequence:
one-half, three-sevenths, one-third, five-nineteenths, three-fourteenths, ...
We can see that each term consists of a numerator and a denominator. The numerator seems to be increasing by a pattern, while the denominator remains constant for each term.
Let's break down the pattern for the numerator:
one-half -> 1
three-sevenths -> 3
one-third -> 1
five-nineteenths -> 5
three-fourteenths -> 3
...
We can observe that the numerator follows the pattern 1, 3, 1, 5, 3, ...
Now let's examine the denominator:
one-half -> 2
three-sevenths -> 7
one-third -> 3
five-nineteenths -> 19
three-fourteenths -> 14
...
The denominator seems to be unrelated to the numerator and varies for each term.
Based on these observations, we can create an explicit formula for the sequence:
an = (numerator)/(denominator)
where the numerator follows the pattern 1, 3, 1, 5, 3, ... and the denominator is the specific denominator given for each term.
Now, to find a14 (the 14th term of the sequence), we can apply the explicit formula. However, we need to know the specific denominator for the 14th term. Unfortunately, the specific denominator is not provided. Without it, we cannot determine the value of a14.
Please provide the denominator for the 14th term, and I will be able to calculate a14 using the explicit formula.