Exercise 16 Page 869

We want to find the number of squares in the tenth step of the given pattern. Let's consider the sequence formed by the number of squares in each step of the pattern.

We can see that, between each step, 2 squares are added to the pattern. Since the difference between the number of squares in each step is constant, the sequence is arithmetic with a common difference of 2. Let's recall the explicit formula of an arithmetic sequence. a_n = a_1 + ( n-1) d Here, a_1 is the first term of the sequence, d is the common difference, and a_n is the nth term in the sequence. In our case, we have 4 squares in the first step. Therefore, a_1 = 4. Let's substitute 2 for d and 4 for a_1 to find the explicit formula of our sequence. a_n = 4 + ( n-1) 2 By substituting 10 for n and simplifying, we can find the number of squares in the tenth step.

The number of squares in the tenth step is 22.