Help with the answers plz

Question

1) Note the pattern shown.

case 1 Case 2 Case 3

2 by 3 units 3 by 4 units 4 by 5 units

a)How many squares would be in the 10th image?

b)How many squares would be in the nth image?

c)What is the rule for this pattern in terms of n?

d)Is the rule arithmetic,geometric, or neither? Explain.

Answer 1

11*12=132

10*11=110

(case#+1)(case#+2)

arith

Answer 2

I'm assuming that the "2 by 3 units" means 2x3 squares for a total of 6 squares.

So we can build this table:

For the rule, it depends on whether you are building a rule for the number of squares of for the number along the length and height. If you are building a rule for the number of squares, it would be the rule shown in the lower right corner:

Where "s" is the total number of squares, and (again), "n" is the case number, then s = n² + 3n + 2.

This is not an arithmetic sequence because to get to the second case, I add 6 to the number of squares in case 1 but I have to add 8 to go from case 2 to case 3.

This is not a geometric sequence either because to go from case 1 to case 2 I multiply by 2 buit to go from case 2 to case 3, I have to multiply by 5/3. So it's neither.