SOLUTION: 2, 12, 36,80,150,? With proper solution

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Question 826918: 2, 12, 36,80,150,? With proper solution
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2, 12, 36,80,150,? With proper solution
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2 = 1^3+1^2
12 = 2^3+2^2
36 = 3^3+3^2
80 = 4^3+4^2
150 = 5^3+5^2
? = 6^3+6^2 = 252
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

use formula
a%5Bn%5D+=+n%5E3%2Bn%5E2 starting with n=1

if n=1
a%5Bn%5D+=+n%5E3%2Bn%5E2
a%5B1%5D+=+1%5E3%2B1%5E2
a%5B1%5D+=+2

if n=2
a%5Bn%5D+=+n%5E3%2Bn%5E2
a%5B2%5D+=+2%5E3%2B2%5E2
a%5B2%5D+=+8%2B4
a%5B2%5D+=+12
if n=3
a%5Bn%5D+=+n%5E3%2Bn%5E2
a%5B3%5D+=+3%5E3%2B3%5E2
a%5B3%5D+=+27%2B9
a%5B3%5D+=+36
:
:
:
so, next term in this sequence will be
if n=6
a%5Bn%5D+=+n%5E3%2Bn%5E2
a%5B6%5D+=+6%5E3%2B6%5E2
a%5B6%5D+=+216%2B36
a%5B6%5D+=+252