Answer:
n^2+3
Step-by-step explanation:
As we can see in the diagram
1st pattern consists from 1 square 1x1 +3 squares 1x1 each
2nd pattern consists from 1 square 2x2 +3 squares 1x1 each
3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each
4-th pattern consists from 1 square 4x4 + 3 squares 1x1 each
We can to continue :
5-th pattern consists from 1 square 5x5+3 squares 1x1 each
So the nth pattern consists from 1 square nxn+3 squares 1x1 each
Or total amount of 1x1 squares in nth pattern N= n^2+3
n² + 3
The first pattern has 4 squares.
The second pattern has 7 squares.
The third pattern has 12 squares.
The fourth pattern has 19 squares.
When we subtract 3 on each term we get:
1, 4, 9, and 16, which are perfect squares.
So n² is in the formula. Each term is added 3 to the perfect squares.
The nth term becomes n² + 3.
C. It is always a rational number. You cannot determine its sign without knowing the values of a and b.
