vladmire wrote:In the finite sequence of positive integers k1,k2,k3,....k9 each term after the second is the sum of the two terms immediately preceding it. If k5 = 18, what is the value of k9
k4 = 11
k6 = 29
a. state 1
b state 2
c both
d each alone
e neither
We have a sequence that follows the rule:
S(n) = S(n-1) + S(n-2)
or, as the stem says, each term is the sum of the two preceding terms.
We know the value of S(5) and we want to solve for S(9).
Well, if we know ANY other term, we can construct the entire sequence.
(1) S(4) = 11
we can add S(4) and S(5) to get S(6), then progress our way up to S(9): sufficient.
(2) S(6) = 29
we can add S(5) and S(6) to get s(7), then progress our way up to S(9): sufficient.
Each of (1) and (2) are sufficient alone: choose (D).
As an aside, the question would have been more interesting (and more difficult) if we had been given terms further away from S(5) in the statements.
For example, if we had been given S(2), we could have set up two equations:
S(2) + S(3) = S(4)
and
S(3) + S(4) = S(5)
Since we know the values of S(3) and S(5), we really have 2 equations and 2 unknowns, so we can solve for everything.
Likewise, if we had been given any other term, we could have set up a series of equations and an equal number of unknowns and solved the entire sequence.
