Question 157358
Number 1 - 1, 8, 27, 64, 125, 216, 343
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The numbers above are the cubes of 1, 2, 3, etc.  The next 3 terms are 512, 729, 1000.
{{{Term n = n^3}}}
Term n = n cubed.
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Number 2 - 2, 5, 14, 41, 122, 365, 1094 
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2, 5, 14, 41, 122, 365, 1094 
Each term is the term before it + 3^n
The next 3 terms are 3281, 9842, 29525
I'll find the algebraic expression later.
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OK, each term in the sum of n terms of 3 to the power of 1 to n, + 1.
The algebraic for the sum of n terms is:
{{{Sum = t1*(1-3^n)/(1-3)}}}
Each term is that plus 1, so it's 
{{{1+(1-3^n)/(-2)}}}
It's not simple.