### 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.

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?

**Solve a Similar Brain Teaser...**

Or, get a random 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.

## 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

## Follow Braingle!