MensaNumber wrote:
In a sequence k, each term after the second term is the sum of the two previous terms. What is the first term of sequence K?
1)one term of sequence K is 29
2)The 4th and 5th terms of K are 11 and 18, respectively
Dear
MensaNumber,
I'm happy to help.
Incidentally, a sequence following this pattern is known as a
Fibonacci sequence. The most famous one, {1, 1, 2, 3, 5, etc.} has deep connections to the Golden Ratio and to many structures in Nature. See:
https://www.goldennumber.net/category/math/In this problem is another Fibonacci sequence.
Statement #1: if we know one term is 29, then it may be that this is the third term, after 14 and 15, or 1 and 28, or -2 and 31, or etc. Or, it may be a later term, the fourth or fifth or sixth, in which case the first term could be almost anything. On the basis of this piece of information, we know nothing.
Statement #2: a4 = 11 and a5 = 18.
We know a3 + a4 = a5, so a3 + 11 = 18, and a3 = 7
Then, we know a2 + a3 = a4, so a2 + 7 = 11, and a2 = 4
Then, we know a1 + a2 = a3, so a1 + 4 = 7, so a1 = 3
This statement, alone and by itself, is sufficient for answering the prompt question.
Answer =
(B)Does all this make sense?
Mike