body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Dashboard

Pearson Algebra 2 Common Core, 2011 View details

2. Arithmetic Sequences

Continue to next subchapter

Exercise 46 Page 576

Does the difference between any two consecutive terms always have the same value?

Recursive Rule: $f (1) = - 32, f (n) = f (n - 1) + 12,$ for $n \geq 2$
Explicit Rule: $f (n) = - 32 + 12 (n - 1),$ for $n \geq 1$

Practice makes perfect

We want write the recursive rule and the explicit rule for the given arithmetic sequence. Let's pay close attention to the difference between two consecutive terms.

- 32 \to + 12 - 20 \to + 12 - 8 \to + 12 4 \to + 12 16 \dots

We can see that the difference between any two consecutive terms is

12 .

Recursive Rule

Let's now consider the general formula for a recursive rule.

f (1) = a f (n) = f (n - 1) + d, for n \geq 2

In the above formula,

a

is the first term of the sequence and

d

is the common difference. For our sequence, the first term is

- 32

and the common difference is

12 .

f (1) = - 32 f (n) = f (n - 1) + 12, for n \geq 2

Explicit Rule

Finally, let's recall the general formula for an explicit rule.

f (n) = a + d (n - 1), for n \geq 1

Again,

a

represents the first term of the sequence and

d

is the common difference. As we have already stated, for our sequence, we have

a = - 32

and

d = 12 .

f (n) = - 32 + 12 (n - 1), for n \geq 1

Subchapter links

Lesson Check p.575

Practice and Problem-Solving Exercises p.575-577

Standardized Test Prep p.577

Mixed Review p.577

Exercise 46 Page 576

Hints

Check the answer

Practice exercises

Asses your skill

Recursive Rule

Explicit Rule