Describe the pattern rule in words, and then with an algebraic expression.

Question

For term one- 4

for term two- 7

for term three- 12

Answer 1

There are really insufficient terms to find a definitive pattern, but going off the fact that the first two terms differ by 3 and the next two terms by 5, we might suspect that the following two terms differ by 7, making the next term 19.
The squares of the natural numbers differ in the same way: 1 4 9 16 ... Add 3 to each of these and we get 4 7 12 19.
Therefore, the algebraic formula for the nth term is n^2+3.