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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 55 Page 280

A sequence is arithmetic if the difference between two consecutive terms is constant.

Is the Sequence Arithmetic? Yes.
Explanation: See solution.
Recursive Formula: $A (n) = A (n - 1) - 4,$ $A (1) = - 3$
Explicit Formula: $A (n) = - 3 + (n - 1) (- 4)$

Practice makes perfect

When a sequence is arithmetic, the difference between two consecutive terms is constant. Examining our sequence we can see that this is the case.

- 3 ⟶ + (- 4) - 7 ⟶ + (- 4) - 11 ⟶ + (- 4) - 15 ⟶ + (- 4) \dots

Since the difference between consecutive terms is constant and equal to

- 4,

we have an arithmetic sequence with common difference

- 4 .

We will use this information to write both the recursive and the explicit formula.

Recursive Formula

Let's recall the general form of the recursive formula for an arithmetic sequence.

Subchapter links

Lesson Check p.278

Practice and Problem-Solving Exercises p.279-281

Standardized Test Prep p.281

Mixed Review p.281