Question

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

Answer 1

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.

Answer 2

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.