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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

7. Arithmetic Sequences

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Exercise 39 Page 279

Can the common difference and the first term be identified just by looking at the recursive formula?

$A (n) = 7.3 + (n - 1) (3.4)$

Practice makes perfect

The explicit formula of an arithmetic sequence combines the information provided by the two equations of the recursive form into a single equation.

Recursive : Explicit : A (n) = A (n - 1) + d; A (1) = A_{1} A (n) = A (1) + (n - 1) d

In these formulas,

d

is the common difference and

A (1)

is the first term. Looking at the given recursive formula, we can identify the common difference

d

and the value of the first term

A_{1} .

A (n) = A (n - 1) + 3.4; A (1) = 7.3

We can see that

3.4

is the common difference and the first term is

7.3 .

Now we have enough information to form an explicit formula for this sequence.

A (n) = A (1) + (n - 1) d

$A (1) = 7.3$ , $d = 3.4$

A (n) = 7.3 + (n - 1) (3.4)

Subchapter links

Lesson Check p.278

Practice and Problem-Solving Exercises p.279-281

Standardized Test Prep p.281

Mixed Review p.281