Exercise 4 Page 155

We are given an arithmetic sequence and asked to write a recursive rule and an explicit rule. 45,55,65,75,... 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)=45. To find d, we calculate the difference between any two consecutive terms. If we look at the first two terms we have that d=55-45=10. We already have all we need to write the recursive rule of the given sequence. f(1)&=45 f(n)&=f(n-1)+10 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)=45 and d=10. Therefore, we have everything we need to write the explicit rule for the given sequence. f(n)=45+10(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.