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What is pyramidal number sequence?
It is a sequence in which the numbers represent the number of spheres in a pyramidal stack of spheres. There are a number of possible configurations for stacking spheres - a visit to fruit stalls may show you options. The square based pyramidal numbers are given by the sums of the first n square numbers. So U(1) = 1^1 = 1 U(2) = 1^2 + 2^2 = 1 + 4 = 5 and so on U(n) = 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6. However, there are also triangle based pyramidal numbers and hexagon based pyramidal numbers, since these configuration also give stable stacks.
How are the sums of Fibonacci added?
The two number before a number are added to get the next number. So if the first numbers are 0,1,1,2,3,5, and 8 for example. You add 0+1=1 which is the third number. 1+1=2 which is the 4th number in the sequence etc. Of course, you can do this forever so the sequence is infinite. In symbols we write the sum as Fn =Fn-1 +Fn-2 The n refers to the nth number in the sequence. For example if n=4, than Fn =2
What is the rule for the Fibonacci numbers sequence?
The Fibonacci sequence(1,1,2,3,5,8,13,21…) is made by the two previous numbers being added together to make the next number. For example 1+1=2, 1+2=3, 2+3=5, 3+5=8 and so on forever…
6 21 40 63 90 121 what is the rule for this sequence?
(1) Take the difference of the two previous numbers in sequence (2) Add 4 to this difference. (3) Take the number from step #2 and add it to the previous number in the sequence. For example, to find the next number in the sequence: (1) 121 - 90 = 31 (2) 31 + 4 = 35 (3) 121 + 35 = 156
What are triangular-numbers?
Triangular numbers are numbers in the sequence 1, 1+2, 1+2+3, 1+2+3+4. This sequence can be represented by triangles as follows: (very crude figure with an even cruder browser!)xxxxxxxxxxxxxxxxxxxxand so on.The nth term of this sequence is n*(n+1)/2.Triangular numbers are numbers in the sequence 1, 1+2, 1+2+3, 1+2+3+4. This sequence can be represented by triangles as follows: (very crude figure with an even cruder browser!)xxxxxxxxxxxxxxxxxxxxand so on.The nth term of this sequence is n*(n+1)/2.
