SOLUTION: 5,6,9,20,?,414 A)96 B)108 C)75 D)192

Question 1119155: 5,6,9,20,?,414
A)96 B)108 C)75 D)192
Found 3 solutions by josgarithmetic, Alan3354, greenestamps:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
Choice D:
192

(Try plotting on cartesian coordinate system. First four points look like a curve; last two points could be a curve but very stretched vertically.)
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Do you have a question?
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

The question is invalid.

Any of the answer choices in the blank will form a valid sequence.

For that matter, ANY number in the blank will form a valid sequence.

Without any context or information as to what kind of sequence this is, it is impossible to find the "right" answer -- in this or ANY OTHER similar problem.

If you consider the sequence as being defined by an explicit formula, then you can always fit n points with a polynomial of degree (n-1)

In this problem there are 5 points defined: (1,5), (2,6), (3,9), (4,20), and (6,414). The five points can be fitted with a polynomial of degree 4:

t(n) = an^4+bn^3+cn^2+dn+e

You can use a graphing calculator or other tool that solves matrices to solve the set of equations that comes from the five given points. Doing that for this set of numbers, the missing number turns out to be 109.8.

So one answer that can be supported with standard mathematics is 109.8.

But again, without any context that says the sequence is defined by a polynomial of degree 4, that answer is no better than any other.
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