Sequences and series

Question

1.) Note the pattern shown below.

1. a. What would the next image look like? Insert it below. 
2. b. How many squares would be in the 10th image? 
3. c. How many squares would be in the nth image?
4. d. What is the rule for this pattern in terms of n? 
5. e. Is the rule arithmetic, geometric, or neither? Explain.

Answer 1

1.a. What would the next image look like? Insert it below. 

Case 4: A rectangular grid 6 x 5.

2.b. How many squares would be in the 10th image? 

Case 10: A rectangular grid 12 x 11 = 132.

3.c. How many squares would be in the nth image?

Case n: A rectangular grid (n+2) x (n+1) = n² + 3n + 2

4.d. What is the rule for this pattern in terms of n? 

t_n = n² + 3n + 2

5.e. Is the rule arithmetic, geometric, or neither? Explain.

Neither. The difference between successive terms is not constant, and the ratio of the difference between successive terms is not constant. However, the difference between the difference between successive terms is constant.