If there is a sequence of numbers 1,4,9,16...... what is the 12th term in the sequence (where 1 is the first term). The textbook says that it is 144 since each term of the sequence is the square of the term value. I find (and have always found) this to be confusing, why can't an alternate algorithm generate those few numbers, namely add 3 for the first term, five to the second term, 7 to the second term. Now there there appears to me an obvious pattern, the amount that one is adding to each term is increasing by 2 in the number of terms. I still haven't figured out an expression for the nth term for this alternative though. The general point though is this, with these sequences if we have given only a few numbers why can't we propose many different algorithms and then suggest that that is the correct generating process?