Found 5 solutions by Edwin McCravy, greenestamps, ikleyn, Plocharczyk, MathTherapy:
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
1+5=6
6+9=15
15+13=28
28+17=45
Looks like we're adding every other odd number, starting with adding 5.
The next odd number after 17 is 19, and the next one after that is 21,
so we'll add 21 to 45 and get the 6th term to be 66.
1+5=6
6+9=15
15+13=28
28+17=45
45+21=66
Edwin
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Although there is an apparent mathematical pattern to the given numbers, the question is actually invalid. ANY next number would make a valid sequence.
ANY problem like this, in which there is no mention of what kind of sequence it is, is invalid for the same reason.
Nevertheless, we can assume that the problem is supposed to be solved using the apparent pattern....
Here is a way to show the process of finding the next number that does exactly the same thing as shown by the other tutor, but in a different way.
1 6 15 28 45 (given sequence)
5 9 13 17 (first differences -- differences between terms of given sequence)
4 4 4 (second differences -- differences between successive first differences)
The constant second differences tell us that the sequence is produced by a polynomial of degree 2. We could go ahead and find that polynomial if we wanted.
But to find the next number in the sequence, we only need to continue the pattern of constant second differences and then work back up the array.
1 6 15 28 45 66
5 9 13 17 21
4 4 4 4
ANSWER: The next number in the sequence (ASSUMING A SEQUENCE GENERATED BY A POLYNOMIAL) is 66.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
For such problems, the question
"Find at least one correct formula for the sequence"
is mathematically correct.
The question "Find the 6-th term" is mathematically NONSENSE.
With such questions, you should go to future-tellers.
/\/\/\/\/\/\/\/
I see some post telling about simplest and most evident formula . . .
Sorry, the original post said NOTHING about it, so your comment is IRRELEVANT.
Also, these arguments lie out of Math.
The FACT is that there are infinitely many formulas, and EVEN INFINITELY MANY POLYNOMIAL formulas
producing given starting values and infinitely many different following terms . . .
So, in this form, the problem DOES NOT RELATE to Math.
It is typical PUZZLE question, with no relation to Math.
Relevant Math problem are formulated differently . . .
Answer by Plocharczyk(17) (Show Source): You can put this solution on YOUR website!
But what is being asked for is the SIMPLEST and MOST OBVIOUS pattern.
Sequences like this are very common on IQ tests and tests given by
companies to employment applicants.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Find the 6th term in the following sequence:
1, 6, 15, 28, 45
Use the following formula for each term:, with "n" being the term number!
This will give you the 6th and ANY other term you need!
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