Question

Pattern A Step 0 Step 1 pattern A or pattern B) shows a quadratic relationship?Step 2 Step 3 8 Pattern B Step 0 Step 1 Step 2 Step 3 2 a. How many dots will there be in Step 4 of each pattern? Pattern A = 16 dots Pattern B = 16 dots b. Which pattern (

Answer 1

Looking at pattern A, the rate at which the number of dots in increasing is linear. The common difference between the number of dots in consecutive steps is 2. The sequence formed is

4, 8, 12.......

The common difference is 8 - 4 = 12 - 8 = 4

Thus, the number of dots in step 4 is

12 + 4 = 16

Looking at pattern B, the sequence formed is

2, 3, 6, 11

3 - 1 = 1

6 - 3 = 3

11 - 6 = 5

We can see that the difference between consecutive terms is increasing by a constant value, 2. This means that the difference between the fourth term and the third term is 5 + 2 = 7

Thus, the number of dots in step 4 is

11 + 7 = 18

b) A quadratic sequence is one in which the second difference between any two consecutive terms is constant. The constant value for the second difference in pattern B is 2

Thus, pattern B is shows a quadratic relationship