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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 49 Page 319

The given rule means that, after the first term of the sequence, every term $f (n)$ is the negative previous term $f (n - 1) .$

$f (2) = - 8$ $f (5) = 8$ $f (10) = - 8$

Practice makes perfect

We are asked to write the

2^{nd},

5^{th}

and

1 0^{th}

term of a sequence, given a recursive rule.

f (1) f (n) = 8 = - f (n - 1), for n > 1

To do so, we will use a table.

$n$	$f (n) = - f (n - 1)$	$f (n)$
$1$	$f (1) = 8$	$8$
$2$	$f (2) = - f (2 - 1)$ $⇕$ $f (2) = - f (1)$	$f (2) = - 8$ $⇕$ $f (2) = - 8$
$3$	$f (3) = - f (3 - 1)$ $⇕$ $f (3) = - f (2)$	$f (3) = - (- 8)$ $⇕$ $f (3) = 8$
$4$	$f (4) = - f (4 - 1)$ $⇕$ $f (4) = - f (3)$	$f (4) = - 8$ $⇕$ $f (4) = - 8$
$5$	$f (5) = - f (5 - 1)$ $⇕$ $f (5) = - f (4)$	$f (5) = - (- 8)$ $⇕$ $f (5) = 8$
$6$	$f (6) = - f (6 - 1)$ $⇕$ $f (6) = - f (5)$	$f (6) = - 8$ $⇕$ $f (6) = - 8$
$7$	$f (7) = - f (7 - 1)$ $⇕$ $f (7) = - f (6)$	$f (7) = - (- 8)$ $⇕$ $f (7) = 8$
$8$	$f (8) = - f (8 - 1)$ $⇕$ $f (8) = - f (7)$	$f (8) = - 8$ $⇕$ $f (8) = - 8$
$9$	$f (9) = - f (9 - 1)$ $⇕$ $f (9) = - f (8)$	$f (9) = - (- 8)$ $⇕$ $f (9) = 8$
$10$	$f (10) = - f (10 - 1)$ $⇕$ $f (10) = - f (9)$	$f (10) = - 8$ $⇕$ $f (10) = - 8$

Therefore, $f (2) = - 8,$ $f (5) = 8$ and $f (10) = - 8 .$

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320