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This printable supports Common Core Mathematics Standard HSF-BF.A.1, HSF-BF.A.1a

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# Sequences as Recursive Functions (Grade 10)

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## Sequences as Recursive Functions

Instructions: For these questions, the set $NN$ does not include zero.

1.
Which of the following recursive functions defines the sequence $5,8,11,14,... ?$ Assume $n in NN$.
1. $t(1) = 3; \ \ t(n) = t(n-1) + 5, \ n>1$
2. $t(1) = 5, \ \ t(n) = t(n-1) - 3, \ n>1$
3. $t(1) = 5, \ \ t(n) = t(n-1) + 3, \ n>1$
4. $t(2) = 8, \ \ t(n) = t(n-2) + 6, \ n>2$
2.
Given the sequence $1,4,16,64,256,...$, which of the following correctly defines this sequence in a recursive form? Assume that $n in NN$.
1. $t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1$
2. $t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1$
3. $t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1$
4. $t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1$
3.
Find the recursive form of the sequence $10, 5, 0, -5, -10,...$ Assume $n in NN$.
1. $t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1$
2. $t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1$.
3. $t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1$.
4. $t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1$
4.
Given the sequence $128, 64, 32, 16, 8, ...$ which of the following functions describes it? Assume $n in NN$.
1. $t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1$
2. $t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1$
3. $t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1$
4. $t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1$
5.
Which of the following functions describes the sequence $18, 31/2, 13, 21/2, 8, ... ?$ Assume that $n in NN$.
1. $t(1) = 18; \ \ t(n) = 43/50 t(n-1), n>1$
2. $t(1) = 18; \ \ t(n) = t(n-1) - 5/2, n>1$
3. $t(1) = 18; \ \ t(n) = t(n-2) - 5, n>2$
4. $t(1) = 18; \ \ t(n) = 5/2 - t(n-1), t>1$
6.
Which of the following functions correctly describe(s) the sequence $3,5,7,9,11,... ?$ Assume that $n in NN$. There may be more than one correct answer.
1. $t(1) = 3; \ \ t(n) = t(n-1) +2, \ n>1$
2. $t(1)=3, \ t(2)=5; \ \ t(n) = t(n-2) + 4, n>2$
3. $t(1) = 3, \ t(2) = 5; \ \ t(n) = -t(n-1) + 2t(n-2) + 6, \ n>2$
4. $t(1) = 3; \ \ t(n+1) = t(n) +2, \ n>=1$
7.
Which recursive function defines the sequence $0, 2, 2, 10, 18, 58, 130, ...$ for $n in N ?$
1. $t(1) = 0; \ \ t(n) = t(n-1) + n-2, \ n>1$
2. $t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4t(n-2), \ n>2$
3. $t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 2t(n-2), \ n>2$
4. $t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4(n-2), \ n>2$
8.
Given the sequence defined by $a(n) = 3 + 5*2^n, \ n in NN, n >=1$, which of the following recursive formulas defines the same sequence? Assume for all sequences that $n in NN$.
1. $t(1) = 13; \ \ t(n) = 3 + 5*2^(n-1), n>1$
2. $t(1) = 13; \ \ t(n) = 2 t(n-1), \ n>1$
3. $t(1) = 13; \ \ t(n) = 13 + t(n-1), \ n>1$
4. $t(1) = 13; \ \ t(n) = -3 + 2t(n-1), \ n >1$
9.
Which of the following functions correctly describes the sequence $1,3,5,9,13,21,...?$ Assume that $n in NN$.
1. $t(1) = 1, t(2) = 3; \ \ t(n) = 2t(n-2) + 3, n>2$
2. $t(1) = 1; \ \ t(n) = t(n-1) + 2, n>1$
3. $t(1)=1, t(2)=3; \ \ t(n) = t(n-2) + t(n-1) + 1, n>2$
4. $t(1) = 1; \ \ t(n) = t(n-1) + 2^(n-1), \ n>1$
10.
Given the sequence $1, -3, -9, -17, -27, ...$, which of the following functions correctly describes it? Assume that $n in NN$.
1. $t(1) = 1, t(2) = -3; \ \ t(n) = t(n-1) - 6t(n-2), n>2$
2. $t(1) = 1; \ \ t(n) = t(n-1) -4, \ n>1$
3. $t(1) = 1; \ \ t(n) = t(n-1) - 2n, \ n > 1$
4. $t(1) = 1; \ \ t(n) = (-1)^(n-1) * 3 * t(n-1), n>1$
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