Exercise 3 Page 155

We are given an arithmetic sequence and asked to write a recursive rule and an explicit rule. 2,0,- 2,- 4,... We will think about these different rules one at time. Then we will find the 20th term of this sequence.

Recursive rule

Let's recall the general form of a recursive rule for an arithmetic sequence. f(1)&=given f(n)&=f(n-1)+d for n > 1 Note that in the above formula d is the common difference. We can see in the given sequence that f(1)=2. To find d, we calculate the difference between any two consecutive terms. If we look at the first two terms we have that d=0-2=- 2. We already have all we need to write the recursive rule of the given sequence. f(1)&=2 f(n)&=f(n-1)-2 for n > 1

Explicit rule

Let's start by recalling the general form of an explicit rule for an arithmetic sequence. f(n)=f(1)+d(n-1) In the above formula, once again d is the common difference. As stated before, we already have f(1)=2 and d=- 2. Therefore, we have everything we need to write the explicit rule for the given sequence. f(n)=2-2(n-1)

Finding the 20th term

To find the 20th term of the sequence we will substitute n=20 to the explicit rule and simplify.