SOLUTION: Trying to find the series for my son's "Chicago Math" 7th grade class. It's an exponetial series with the following (x,y) points (1,1), (2,3), (3,6), (4,10), (nth,?). Help if yo

Algebra ->  Sequences-and-series -> SOLUTION: Trying to find the series for my son's "Chicago Math" 7th grade class. It's an exponetial series with the following (x,y) points (1,1), (2,3), (3,6), (4,10), (nth,?). Help if yo      Log On


   

Question 156348: Trying to find the series for my son's "Chicago Math" 7th grade class. It's an exponetial series with the following (x,y) points (1,1), (2,3), (3,6), (4,10), (nth,?).
Help if you can, Thanks!
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
exponetial series with the following (x,y) points (1,1), (2,3), (3,6), (4,10), (nth,?
-----------------
Exponential Form: y = ab^x
You need to determine a and b.
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Substitute x and y from any two points to get two equaitons:
1 = ab^1
6 = ab^3
--------------
Divide the 1st into the 2nd
6 = b^2
b = sqrt(6)
----------------
Substitute to solve for "a":
1 = a(sqrt(6))^1
a = 1/sqrt(6)
a = 0.408248
----------------------
EQUATION:
y = (0.408248)(sqrt(6))^x
===============================
Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I was looking at this problem trying to "see" the series.
I don't see it as an "exponential" series.
What I do see is that each y-value is the sum of all the previous x-values.
This can be expressed as:
highlight%28y+=+%28%28x%5E2%2Bx%29%29%2F2%29
To try a few values: x = 1:
y+=+%281%5E2%2B1%29%2F2
y+=+%281%2B1%29%2F2
y+=+1
For x = 3:
y+=+%283%5E2%2B3%29%2F2
y+=+%289%2B3%29%2F2
y+=+12%2F2
y+=+6
For x = 4:
y+=+%284%5E2%2B4%29%2F2
y+=+%2816%2B4%29%2F2
y+=+20%2F2
y+=+10
So on this basis, the nth term would be:
highlight%28y%5Bn%5D+=+%28%28n%5E2%2Bn%29%29%2F2%29