Solve the following problem

Algebra Level pending

Find for N N ,

0 , 1 , 3 , 6 , 10 , 15 , 21 , 28 , N 0, 1, 3, 6, 10, 15, 21 ,28, N

Note : This is not a geometric progression nor a arithmetic progression .

Hint : It will help to stack cups.

These number don't have a relationship 30 49 36

Rex Holmes by Rex Holmes , 17, USA

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3 solutions

Rex Holmes
Aug 22, 2016

What I meant when I said it would help to stack cups is literally stack cups if you stack cup towers of different sizes you get the sequence in the above problem 0, 3, 6, 10, 15... as you may have also notice 6-3=3 10-6=4 15-10=5 and so on suggesting a pattern.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Please update your solution. Thanks.

Calvin Lin Staff - 4 years, 9 months ago
Goh Choon Aik
Aug 26, 2016

These numbers are triangle numbers.

T n = T n − 1 + n T _n = T_{n-1} + n

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Here its better to explain serial number wise,

0-0 = 0

1-0 = 1

3-1 = 2

6-3 = 3

10-6 = 4

15-10 = 5

21-15 = 6

28-21= 7

N-28 = 8

For N = 28+8 = 36

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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