What is the nth term of the sequence: 3,11,25,45
i know it begins with 3n^2
i entered 3n^2-(n-1) and it marked it as incorrect?: )

This solution might be a bit out there, but it should probably work.

For this, we will consider sequences to have an invisible "0th" term to make calculation easier.

For the simple sequence {0}, 1, 3, 6, 10,... ({0}+1=1, 1+2=3, 3+3=6, 6+4=10,...), the general formula is

Note the bold number increases by 1 each time.

We have {number}, 3, 11, 25, 45,... (3+8=11, 11+14=25, 25+20=45,...)
The bold number increases by 6 each time.

So we consider next: {0}, 6*1, 6*3, 6*6, 6*10,... ({0}+6=6, 6+12=18, 18+18=36, 36+24=60,...) and we get


From the 1st term to the 2nd term, this sequence has an increase of 12.

But we want it to have an increase of 8, so we subtract 4 from each bold number.

({0}+2=2, 2+8=10, 10+14=24, 24+40=64,...)

From each bold number, we have subtracted 4, so each term decreases by .

We now have


But instead of {number}, 2, 10, 24, 44,..., we want {number}, 3, 11, 25, 45,... So we add 1 to each term and get


Now we expand this expression out:


So remove the parentheses and make the 1 positive.

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