Question

A) Describe the following sequence

in words:
2, 2, 4, 6, 10, 16, 26, ...
b) Could 947 be a term in the sequence?
Explain.
c) Compare the square of the 4th term
with the product of the previous term
(3rd term) and the following term
(5th term). Describe the relationship.
Is this relationship valid for other
terms in the sequence?
d) How does the relationship in part (c)
compare with the relationship between
the square of a term and the product of
the previous and following terms of
the Fibonacci sequence?

Answer 1

Explanation:

Compare the square of the 4th term with the product of the previous term (3rd term) and the following term (5th term). Describe the relationship. Is this relationship valid for other terms in the sequence?

Answer 2

A) The pattern is adding the first number to the previous one, the pattern goes like this: 0 + 2 = 2, 2 + 2 = 4, 2 + 4 = 6, 5 + 6 = 10 etc.

B) No, because this sequence cannot have odd numbers

C) The products of 3 (4) and 5 (10) is 40, while the square of 6 is 36, it seems that when you take an even numbered term, (2nd, 4th, 6th, 8th etc.) and square it, and also multiply both odd terms to its right and left, the squared term will always be 4 less than the multiplied terms.

D) Since this sequence just seems to be the FIbo sequence multiplied by 2, we can safely say that it will be half of that. The squared term will always be 2 less than the multiplied terms.