Brain Teasers
What is the Next Number?
Series
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.Series
What is the next number in this series?
6, 14, 36, 98, 276, ...
6, 14, 36, 98, 276, ...
Hint
This is not an obvious series. Summation notation is required to solve this teaser.Answer
794The nth term in the series is given by the sum of x^n for x in the range 1 to 3, i.e. 1^n + 2^n + 3^n.
Thus the first term is 1^1 + 2^1 + 3^1 = 1 + 2 + 3 = 6,
the second term is 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14,
and so on.
The sixth term is then 1^6 + 2^6 + 3^6 = 1 + 64 + 729 = 794.
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
Very good! Or how about this?
If n is the ordinal value of the term in the series, then the nth term in the series is
the (n-1)th term * 3 - (2 + 2^(n-1)), given that the first term is provided as 6.
So the second term is: 6 * 3 - (2 + 2^(2-1)) = 18 - (2 + 2^1) = 18 - (2 + 2) = 18 - 4 = 14,
the third term is: 14 * 3 - (2 + 2^(3-1)) = 42 - (2 + 2^2) = 42 - (2 + 4) = 42 - 6 = 36,
the fourth term is: 36 * 3 - (2 + 2^(4-1)) = 108 - (2 + 2^3) = 108 - (2 + = 108 - 10 = 98,
the fifth term is: 98 * 3 - (2 + 2^(5-1)) = 294 - (2 + 2^4) = 294 - (2 + 16) = 294 - 18 = 276, and
the next (6th) term is: 276 * 3 - (2 + 2^(6-1)) = 828 - (2 + 2^5) = 828 - (2 + 32) = 828 - 34 = 794.
If n is the ordinal value of the term in the series, then the nth term in the series is
the (n-1)th term * 3 - (2 + 2^(n-1)), given that the first term is provided as 6.
So the second term is: 6 * 3 - (2 + 2^(2-1)) = 18 - (2 + 2^1) = 18 - (2 + 2) = 18 - 4 = 14,
the third term is: 14 * 3 - (2 + 2^(3-1)) = 42 - (2 + 2^2) = 42 - (2 + 4) = 42 - 6 = 36,
the fourth term is: 36 * 3 - (2 + 2^(4-1)) = 108 - (2 + 2^3) = 108 - (2 + = 108 - 10 = 98,
the fifth term is: 98 * 3 - (2 + 2^(5-1)) = 294 - (2 + 2^4) = 294 - (2 + 16) = 294 - 18 = 276, and
the next (6th) term is: 276 * 3 - (2 + 2^(6-1)) = 828 - (2 + 2^5) = 828 - (2 + 32) = 828 - 34 = 794.
Simply :
Other possibility :
1) Calculate the difference between the two consecutive numbers:
14 - 6 = 8
36 - 14 = 22
98 - 36 = 62
276 - 98 = 178
2) Find the pattern between the differences :
_ 8*3 = 24 - (2) = 22
_ 22*3 = 66 - (4) = 62
_ 62*3 = 186 - ( = 178
3) Notice the number between parantheses are the direct multiplication of the precedent by *2.
The next number would be :
_ 178*3 = 534 - (16) = 518
_________
The next number in the series is :
276 + 518 = 794, your answer
Other possibility :
1) Calculate the difference between the two consecutive numbers:
14 - 6 = 8
36 - 14 = 22
98 - 36 = 62
276 - 98 = 178
2) Find the pattern between the differences :
_ 8*3 = 24 - (2) = 22
_ 22*3 = 66 - (4) = 62
_ 62*3 = 186 - ( = 178
3) Notice the number between parantheses are the direct multiplication of the precedent by *2.
The next number would be :
_ 178*3 = 534 - (16) = 518
_________
The next number in the series is :
276 + 518 = 794, your answer
This is a terrific teaser! I actually came up with the same algorithm as ThinksForFun. When I saw the answer I kicked myself twice for not seeing that pattern. Outstanding series teaser! Well done.
It is interesting the lengths we'll go to to find a solution when the simple solution eludes us.
It is interesting the lengths we'll go to to find a solution when the simple solution eludes us.
To post a comment, please create an account and sign in.
Follow Braingle!