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This printable supports Common Core Mathematics Standard HSF-BF.A.2

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# Translating Between Forms of Geometric Sequences (Grade 10)

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## Translating Between Forms of Geometric Sequences

1.
For the geometric sequence defined by $a_n = 3*2^(n-1)$, what is its recursive formula?
1. $a_1 = 1; \ \ a_n = 2a_{n-1}, \ n>1$
2. $a_1 = 3; \ \ a_n = 2a_{n-1}, \ n>1$
3. $a_1 = 1; \ \ a_n = 3a_{n-1}, \ n>1$
4. $a_1 = 2; \ \ a_n = 3a_{n-1}, \ n>1$
2.
If the explicit form of geometric sequence is $a_n = 4^n$, what is its recursive form?
1. $a_1 = 0; \ \ a_n = 4a_{n-1}, n>1$
2. $a_1 = 1; \ \ a_n = 4a_{n-1}, \ n>1$
3. $a_1 = 4; \ \ a_n = 4n \ a_{n-1}, \ n>1$
4. $a_1 = 4; \ \ a_n = 4a_{n-1}, \ n>1$
3.
What is the recursive form of the the geometric sequence defined by $a_n = -5*3^{n-1} ?$
1. $a_1 = -5; \ \ a_n = 3a_{n-1}, \ n>1$
2. $a_1 = -15; \ \ a_n = 3a_{n-1}, \ n>1$
3. $a_1 = 3; \ \ a_n = -5a_{n-1}, \ n>1$
4. $a_1 = 1; \ \ a_n = 5a_{n-1}, \ n>1$
4.
Given the geometric sequence defined by $a_n = 1/8 * 8^n$, what is the recursive form of this sequence?
1. $a_1 = 1; \ \ a_n = 8a_{n-1}, \ n>1$
2. $a_1 = 1/8; \ \ a_n = 8a_{n-1}, \ n>1$
3. $a_1 = 8; \ \ a_n = 8a_{n-1}, \ n>1$
4. $a_1 = 8; \ \ a_n = 1/8 a_{n-1}, \ n>1$
5.
For the geometric sequence defined by $a_n = 1/4 * (4/3)^n$, what is the recursive form of the this sequence?
1. $a_1 = 1; \ \ a_n = 4/3 a_{n-1}, \ n>1$
2. $a_1 = 1/4; \ \ a_n = 1/3 a_{n-1}, \ n>1$
3. $a_1 = 1/4; \ \ a_n = 4/3 a_{n-1}, \ n>1$
4. $a_1 = 1/3; \ \ a_n = 4/3 a_{n-1}, \ n>1$
6.
For the geometric sequence defined by $a_1 = 80; \ \ a_n = 1/2 a_{n-1}, n>1$, what is the explicit form of this sequence?
1. $a_n = 80(1/2)^n$
2. $a_n = 80(1/2)^(n-1)$
3. $a_n = 80*2^(n-1)$
4. $a_1 = 1*(1/2)^n$
7.
What is the recursive form of the sequence defined by $a_1 = 2; \ \ a_n = 5 a_{n-1}, \ n>1 ?$
1. $a_n = 2*5^n$
2. $a_n = 2*5^(n+1)$
3. $a_n = (2/5)*5^n$
4. $a_n = (2/5)*5^(n-1)$
8.
Given the recursive form of the sequence $a_1 = 2/7; \ \ a_n = 3a_{n-1}, \ n>1$, find the correct explicit form of this sequence.
1. $a_n = 2/21 * 3^n$
2. $a_n = 2/7 * 3^n$
3. $a_n = 2/7 * 3n$
4. $a_n = (6/7)^{n-1}$
9.
What is the explicit form of the sequence defined by $a_1 = 1/2; \ \ a_n = 1/2 a_{n-1}, \ n>1 ?$
1. $a_n = (1/2)^{n-1}$
2. $a_n = (1/2)*(1/2)^(-n)$
3. $a_n = (1/2)^n$
4. $a_n = 1/2 * (1/2)^n$
10.
For the sequence defined by $a_1 = 100; \ \ a_n = -1/5 a_{n-1}, \ n>1$, what is the explicit form of this sequence? There may be more than one correct answer.
1. $a_n = 100*(-1/5)^{n-1}$
2. $a_n = -500*(-1/5)^{n}$
3. $a_n = 100*(-1/5)^n$
4. $a_n = (-1)^n*(-500)*(5)^{-n}$
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