Question 395408: Hello,
What is the 6th number of the next series? and why?
1,4,9,36,41, ....
Thank you very much!
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! There are many ways to do this, but one way is to look for a repeating pattern.
Often you'll have a pattern involving 2 arithmetic operations. In this case, we're dealing with multiplication and addition.
The jump from 1 to 4 is multiplying 1 by 4 to get 4.
To go from 4 to 9, we're adding 5
To get to 36 from 9, we're multiplying by 4 (starting to see the pattern?)
To go from 36 to 41, we're adding 5
So the next move is to multiply 41 by 4 to get 41*4 = 164
So the 6th number is 164.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my tutoring website
Jim
Answer by Edwin McCravy(20064)  (Show Source):
You can put this solution on YOUR website!
The other tutor thought of an easier pattern than I saw. I didn't
think of an alternating pattern like that, where you do 1 thing one
time and do another thing the next time. This one is also correct
and works. Actually there are an infinite number of patterns.
Write the numbers in a column:
1
4
9
36
41
Subtract each of the first 4 numbers in that column from the one
just below it and write the answer to the right of that number:
1 3
4 5
9 27
36 5
41
Subtract each of the first 3 numbers in that 2nd column from the one
just below it and write the answer to the right of that number:
1 3 2
4 5 22
9 27 -22
36 5
41
Subtract each of the first 2 numbers in that 1st column from the one
just below it and write the answer to the right of that number:
1 3 2 20
4 5 22 -44
9 27 -22
36 5
41
Subtract the 20 from the -44 just below it, getting -66 and
writing that beside the 20:
1 3 2 20 -66
4 5 22 -44
9 27 -22
36 5
41
Now write another -66 under that one
1 3 2 20 -66
4 5 22 -44 -66
9 27 -22
36 5
41
Add the bottom -66 to the -44, getting -110 and write that
under the -44
1 3 2 20 -66
4 5 22 -44 -66
9 27 -22 -110
36 5
41
Add the -110 to the -22, getting -132, and write that
under the -22
1 3 2 20 -66
4 5 22 -44 -66
9 27 -22 -110
36 5 -132
41
Add the -132 to the 5, getting -127, and write that
under the 5.
1 3 2 20 -66
4 5 22 -44 -66
9 27 -22 -110
36 5 -132
41 -127
Add the -127 to the 41, getting -86 and write that
under the 41
1 3 2 20 -66
4 5 22 -44 -66
9 27 -22 -110
36 5 -132
41 -127
-86
So the 6th term term is -86
Want a general formula?
Edwin
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