Translating Between Forms of Arithmetic Sequences (Grade 9)

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Translating Between Forms of Arithmetic Sequences

1. 
Given the explicit form of the arithmetic sequence [math]a_n = -2 + 7n[/math], which of the following is the recursive formula for the same sequence?
  1. [math]a_1 = 5; \ \ a_n = a_{n-1} + 7, \ n>1[/math]
  2. [math]a_1 = 5; \ \ a_n = a_{n-1} - 2, \ n>1[/math]
  3. [math]a_1 = -2; \ \ a_n = a_{n-1} +7, \ n>1[/math]
  4. [math]a_1 = -2; \ \ a_n = a_{n-1} - 2, n>1[/math]
2. 
What is the recursive form of the sequence [math]a_n = 16-20n ?[/math]
  1. [math]a_1 = -20; \ \ a_n = a_{n-1} + 16, \ n>1[/math]
  2. [math]a_1 = 16; \ \ a_n = a_{n-1} - 20, \ n>1[/math]
  3. [math]a_1 = -4; \ \ a_n = a_{n-1} + 16, \ n>1[/math]
  4. [math]a_1 = -4; \ \ a_n = a_{n-1} - 20, \ n>1[/math]
3. 
For the sequence defined by the explicit formula [math]a_n = 7 + 3n[/math], what is the the recursive formula for this sequence?
  1. [math]a_1 = 7; \ \ a_n = a_{n-1} + 3, \ n>1[/math]
  2. [math]a_1 = 10; \ \ a_n = a_{n-1} + 3, \ n>1[/math]
  3. [math]a_1 = 3; \ \ a_n = a_{n-1} + 7, \ n>1[/math]
  4. [math]a_1 = 1; \ \ a_n = a_{n-1} + 7, \ n>1[/math]
4. 
What is the recursive form of the sequence given by [math]a_n = 33 - 4n ?[/math]
  1. [math]a_1 = 33; \ \ a_n = a_{n-1} - 4, \ n>1[/math]
  2. [math]a_1 = -4; \ \ a_n = a_{n-1} +1, \ n>1[/math]
  3. [math]a_1 = 29; \ \ a_n = a_{n-1} - 4, \ n>1[/math]
  4. [math]a_1 = 33; \ \ a_n = a_{n-1} - 4n, \ n>1[/math]
5. 
For the sequence defined by [math]a_n = 2n[/math], how could the same sequence be written recursively? There may be more than one answer.
  1. [math]a_1 = 2; \ \ a_n = a_{n-1} + 2, \ n>1[/math]
  2. [math]a_1 = 0; \ \ a_n = a_{n-1} + 2, \ n>1[/math]
  3. [math]a_1 = 0, a_2 = 2; \ \ a_n = a_{n-2} + 2, \ n>2[/math]
  4. [math]a_1 = 2, a_2 = 4; \ \ a_n = a_{n-2} + 4, \ n>2[/math]
6. 
For the sequence defined by [math]a_1 = 3; \ \ a_n = a_{n-1} + 5, \ n>1[/math], what is its explicit form?
  1. [math]a_n = 3 - 5n[/math]
  2. [math]a_n = -2 + 5n[/math]
  3. [math]a_n = 5 - 3n[/math]
  4. [math]a_n = 1 - 2n[/math]
7. 
What is the explicit form of the sequence defined by [math]a_1 = 0; \ \ a_n = a_{n-1} + 3, \ n>1 ?[/math]
  1. [math]a_n = 3 + 3n[/math]
  2. [math]a_n = 3n[/math]
  3. [math]a_n = -3 + n[/math]
  4. [math]a_n = -3 + 3n[/math]
8. 
Given the arithmetic sequence defined by [math]a_1 = -10; \ \ a_n = a_{n-1} + 10, \ n>1[/math], what is the explicit form of this sequence?
  1. [math]a_n = 10n[/math]
  2. [math]a_n = -10 + 10n[/math]
  3. [math]a_n = 10 - 10n[/math]
  4. [math]a_n = -20 + 10n[/math]
9. 
Find the explicit formula of the sequence defined by [math]a_1 = 85; \ \ a_n = a_{n-1} - 15, \ n>1[/math].
  1. [math]a_n = 85 - 15n[/math]
  2. [math]a_n = -15 + 100n[/math]
  3. [math]a_n = 100 - 15n[/math]
  4. [math]a_n = 85 - 100n[/math]
10. 
For the sequence defined by [math]a_1 = 4; \ \ a_n = a_{n-1} - 4, n>1[/math], which of the following describes the same sequence? There may be more than one correct answer.
  1. [math]a_n = 8-4n[/math]
  2. [math]a_n = 4 - 4(n-1)[/math]
  3. [math]a_n = 4 - 4n[/math]
  4. [math]a_n = -4 - 4(n-3)[/math]

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