SOLUTION: How do i find the sequences -5, 3, -2, 1, -1, 0 and 1, 5, 14, 30, 55

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Question 1092849: How do i find the sequences -5, 3, -2, 1, -1, 0 and 1, 5, 14, 30, 55
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

You can NEVER be sure of the right answer to any problem like this, because any next number, or next sequence of 2 or 3 or more numbers, is a valid sequence.

However, in each of these sequences there is a nice pattern which makes it possible to find what is PROBABLY the rule for producing the sequence.

In both of the sequences, look at what you have to add to each term to get the next term. Then look for a pattern in those numbers that you have to add.

first sequence...

-5 + 8 = 3
3 + -5 = -2
-2 + 3 = 1
1 + -2 = -1
-1 + 1 = 0

The sequence of numbers you have to add (the sequence of numbers in the middle column) is
8, -5, 3, -2, 1, ...

Do you see a pattern there? (hint: look at the original sequence....)

second sequence...

This one is easy, when you look at it the right way:

1 + 4 = 5
5 + 9 = 14
14 + 16 = 30
30 + 25 = 55

Do you see the pattern in the numbers in the second column?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
 -5, 3, -2, 1, -1, 0 

Each term after the first two is the sum of the two preceding terms:

(-5) +  (3) = (-2)
 (3) + (-2) =  (1)  
(-2) +  (1) = (-1)
 (1) + (-1) =  (0)
(-1) +  (0) = (-1)
 (0) + (-1) = (-1)
(-1) + (-1) = (-2)
etc.  [Beginning with the 5th term it becomes the 
negatives of the Fibbonacci sequence]

The general term is




and 


1, 5, 14, 30, 55 

That's the sum of the squares

1² = 1
1²+2² = 1+4 = 5
1²+2²+3² = 1+4+9 = 14
1²+2²+3²+4² = 1+4+9+16 = 30
1²+2²+3²+4²+5² = 1+4+9+16+25 = 55

The general term is



Edwin
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