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

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