SOLUTION: My daughter has 2 homework problems that she asked for my help on but I am stumped. The directions are to add 3 terms to each pattern and then write an algebraic expression that d

Question 157358: My daughter has 2 homework problems that she asked for my help on but I am stumped. The directions are to add 3 terms to each pattern and then write an algebraic expression that describes the pattern. She can add the terms to the pattern (see the last 3 numbers in each line below) but we are stumped on the expression that goes with it.
Number 1 - 1, 8, 27, 64, 125, 216, 343
Number 2 - 2, 5, 14, 41, 122, 365, 1094
Thanks for your help!
Answer by Alan3354(21584) (Show Source):
You can put this solution on YOUR website!
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 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:

Each term is that plus 1, so it's

It's not simple.