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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

2. Arithmetic Sequences

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Exercise 80 Page 577

Does the formula describe the $n^{th}$ term using the number $n ?$ Does it relate consecutive terms?

Explicit or Recursive? Explicit.
First Five Terms: $a_{1} = 0,$ $a_{2} = 3,$ $a_{3} = 8,$ $a_{4} = 15$ and $a_{5} = 24$

Practice makes perfect

An explicit formula describes the

n^{th}

term of a sequence using the number

n .

A recursive formula relates consecutive terms. Consider the given formula.

a_{n} = n^{2} - 1

This formula describes the

n^{th}

term using the number

n .

Therefore, it is an explicit formula. Let's use it to find the first five terms of the sequence.

$n$	$n^{2} - 1$	$a_{n} = n^{2} - 1$
$1$	$1^{2} - 1$	$a_{1} = 0$
$2$	$2^{2} - 1$	$a_{2} = 3$
$3$	$3^{2} - 1$	$a_{3} = 8$
$4$	$4^{2} - 1$	$a_{4} = 15$
$5$	$5^{2} - 1$	$a_{5} = 24$

Subchapter links

Lesson Check p.575

Practice and Problem-Solving Exercises p.575-577

Standardized Test Prep p.577

Mixed Review p.577