Subject Test Math 2

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Subject Test Math 2

Question 11 of 28

A sequence is recursively defined by $a_{n} = a_{n - 1} + 2 a_{n - 2}$ , for $n > 2$ . If $a_{1} = 0$ and $a_{2} = 1$ , what is the value of $a_{6}$ ?

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$5$

Correct Answer:

No

$8$

Correct Answer:

No

$11$

Correct Answer:

Yes

$13$

Correct Answer:

No

$21$

Correct Answer:

No

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The values for $a_{1}$ and $a_{2}$ are given. $a_{3}$ is equal to $a_{2} + 2 a_{1} = 1 + 0 = 1$ . $a_{4}$ is equal to $a_{3} + 2 a_{2} = 1 + 2 (1) = 3$ . $a_{5}$ is equal to $a_{4} + 2 a_{3} = 3 + 2 (1) = 5$ . $a_{6}$ is equal to $a_{5} + 2 a_{4} = 5 + 2 (3) = 11$ .

If your graphing calculator has a sequence mode, you can define the sequence recursively and find the value of $a_{6}$ . Let $n Min = 1$ , since the first term is $a_{1}$ . Define $u (n) = u (n - 1) + 2 u (n - 2)$ . Let $u (n Min) = {1, 0}$ , since we have to define the first two terms $a_{1}$ and $a_{2}$ . Then examining a graph or table, you can find $u (6)$ .

Question Difficulty:

medium

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Subject Test Math 2

Question 11 of 28

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View Correct Answer