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I'm trying to find the pattern here. What would the number possibly be in place of "x"?

7, 19, X, 4.

Can the number be within the range of 1-26?

Thanks!

Hello,

Problems like these are questionable without some kind of idea or theme.

The reason is that there are infinitely many "correct" answers (usually

only one "simplest" answer though).

I'll use this problem as an example. Since we are given 3 values, I assumed

the sequence has a form f(n)=a*n^2 + b*n +c, where a,b, and c are constants

with f(1)=7, f(2)=19, f(3)=x=?, and f(4)=4. Using the known values, we get 3

equations for a, b, and c:

f(1)=7 gives: a+b+c=7, f(2)=19 gives: 4a+2b+c=19, and f(4)=4 gives: 16a+4b+c=4.

Solving these three equations for a, b, and c gives: a=-13/2, b=63/2, and c=-18.

Thus, one possible solution is: f(n)=(-13/2)n^2+(63/2)n-18 = (1/2)(63n-13n^2-36).

Now use this to determine f(3)...f(3)=(1/2)(189-117-36)=18. So 18 is a fine answer!

However, what if we use a different model, say f(n)=a*n+b/n+c. This model gives

a=-14, b=-52, and c=73 to get: f(n)=73-14n-52/n. Now let n=3 to get f(3)=41/3, which

is also "a correct answer." See what I mean?

Probably, the person who made the problem had the first way in mind, so f(3)=18.

But, who knows??!!!!

A. Mantell

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Comment | Thank you! Very detailed, much appreciated. |

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Over 15 years teaching at the college level.**Organizations belong to**

NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.**Education/Credentials**

B.S. in Mathematics from Rensselaer Polytechnic Institute

M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook