Question 1203845: 20, 32, 47, 57, ?, 80
Find the missing number of the given series
Found 4 solutions by josgarithmetic, greenestamps, math_tutor2020, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Differences between successive pairs
12, 15, 10, something, somethingelse
Try any two-digit number between 57 and 80 not including them. Otherwise no specific pattern.
The best possible answers for the unknown term are any one of:
67, 68, 69, 70.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
There is no mathematics to this; it is purely entertainment.
ANY number in the missing spot makes a valid sequence.
If there is no information given about what kind of sequence it is, then it is only a guessing game.
Spend as much (or, better yet, as little!) time as you want trying to find a pattern that predicts the missing number -- knowing that any "answer" you come up with might not be "right".
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Since you have received several responses saying that it's not possible to know the answer, I will add to my response to show that there is a formal mathematical way to find ONE POSSIBLE answer to the problem.
The problem shows terms 1, 2, 3, 4, and 6 of a sequence. We can find a solution using formal mathematics if we assume that the sequence is generated by a polynomial function. If we do that, then we are looking for a polynomial f(x) for which
f(1)=20; f(2)=32; f(3)=47; f(4)=57; and f(6)=80
5 known function values can be fitted with a unique polynomial of degree 4, so we are looking for a function
that has the 5 given function values.
We can use matrices (e.g., on a graphing calculator like a TI-83 or TI-84) to find the polynomial function that generates the given function values. Doing that gives us the following polynomial:
We can then find the missing number in the sequence by evaluating f(5), which turns out to be 64.
So ONE POSSIBLE answer to the problem, using a formal mathematical process is 64.
We can also find that answer, without finding the polynomial that generates the sequence, using the method of finite differences. In a polynomial of degree 4, the 4th differences are constant.
So we can call the missing term x and find the 4th differences and set them equal to find the missing term.
20 32 47 57 x 80 given terms
12 15 10 x-57 80-x 1st differences
3 -5 x-67 137-2x 2nd differences
-8 x-62 204-3x 3rd differences
x-54 266-4x 4th differences
The 4th differences must be the same:
Answer by math_tutor2020(3817) (Show Source):
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
Submitting such problems under the guise of mathematical problems is EITHER
(a) a form of 100% cheating;
OR
(b) a form of 100% misunderstanding what a Math problem is, in general.
So, if you want to maintain your good name and reputation, never participate in disseminating of such tasks.
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