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Subject Test Math 2

Question 11 of 28

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SAT Subject Test

A sequence is recursively defined by a subscript n end subscript invisible times equals a subscript n minus 1 end subscript invisible times plus 2 a subscript n minus 2 end subscript, for n invisible times greater than 2. If a subscript 1 end subscript invisible times equals 0 and a subscript 2 end subscript invisible times equals 1, what is the value of a subscript 6 end subscript?

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5

Correct Answer: 
No

8

Correct Answer: 
No

11

Correct Answer: 
Yes

13

Correct Answer: 
No

21

Correct Answer: 
No

The values for a subscript 1 end subscript and a subscript 2 end subscript are given. a subscript 3 end subscript is equal to a subscript 2 end subscript invisible times plus 2 a subscript 1 end subscript invisible times equals 1 invisible times plus 0 invisible times equals 1. a subscript 4 end subscript is equal to a subscript 3 invisible times end subscript invisible times plus 2 a subscript 2 end subscript invisible times equals 1 invisible times plus 2 left parenthesis 1 right parenthesis equals 3. a subscript 5 end subscript is equal to a subscript 4 invisible times end subscript invisible times plus 2 a subscript 3 end subscript invisible times equals 3 invisible times plus 2 left parenthesis 1 right parenthesis equals 5. a subscript 6 end subscript is equal to a subscript 5 end subscript invisible times plus 2 a subscript 4 end subscript invisible times equals 5 invisible times plus 2 left parenthesis 3 right parenthesis equals 11.

If your graphing calculator has a sequence mode, you can define the sequence recursively and find the value of a subscript 6 end subscript. Let n invisible times text Min = 1 end text, since the first term is a subscript 1 end subscript. Define u left parenthesis n right parenthesis invisible times equals u left parenthesis n invisible times minus 1 right parenthesis invisible times plus 2 u left parenthesis n invisible times minus 2 right parenthesis. Let u left parenthesis n invisible times text Min end text right parenthesis invisible times equals left curly bracket 1 comma 0 right curly bracket, since we have to define the first two terms a subscript 1 end subscript and a subscript 2 end subscript. Then examining a graph or table, you can find u left parenthesis 6 right parenthesis.

Question Difficulty: 
medium