SOLUTION: Solve the series 5 10 15 34 60 61 ?

Question 1090865: Solve the series
5 10 15 34 60 61 ?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There is no way to "solve" any problem like this.

Any sequence of numbers is a valid sequence; so you could put any number you want next and this would be a valid sequence.

In some such problems, there is enough evidence with the given numbers to figure out what is LIKELY TO BE the next number; but there is no way to know for sure.

Any finite sequence of n numbers can be produced by a polynomial function of degree (n-1). 2 numbers give you a polynomial of degree 1 (think of it as 2 points determining a line). 3 numbers can be produced by a quadratic polynomial (degree 2). 4 numbers can be produced by a cubic polynomial, 5 numbers by a polynomial of degree 4, and -- as in your example -- 6 numbers by a polynomial of degree 5.

So you could take the general polynomial of degree 5...

... and form 6 equations by setting P(1)=5, P(2)=10, ..., and P(6)=61. You can then solve that system of 6 equations in 6 unknowns to determine the particular polynomial that produces your sequence.

That method will always give you "A" solution for the sequence. But there is never any way to know if that is the "right" answer according to the author of the problem.

Whenever I see a problem like this, I spend a very short time trying to see if I can see a nice pattern in the numbers; if not, I drop the problem, knowing I have better things to do with my time.
RELATED QUESTIONS
Find the value of the series... (answered by Fombitz,MathLover1)

complete the series B+5,D-10,... (answered by fractalier)

calculate the average age of migrants for both the categories of gender and write your... (answered by ikleyn)

Use summation notation to write the series 49 + 55 + 61 + ... for 10... (answered by vleith)

Number Series: 5, 6, 10, 19, 35, 60, ___ Please give the solution. Thank... (answered by Alan3354)

Find the sum of the first 10 terms of the series:... (answered by stanbon)

what is the next number in the series 5 10 15 25 40... (answered by sachi)

What comes next in the series 15, 13, 10, 8, 5,... (answered by stanbon)

Find the sum of the first 10 terms of the series defined by the formula: an = -2n +... (answered by stanbon)