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Ninth Grade (Grade 9) Sequences and Series Questions

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Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series
The difference between any two consecutive terms in an arithmetic sequence.
  1. Repetitive Change
  2. Common Difference
  3. Sequence
Grade 9 Sequences and Series
Each number in a sequence.
  1. Sequence
  2. Term
  3. Arithmetic Sequence
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
Which of the following is the explicit formula for the arithmetic sequence -1, 1, 3, 5, ... ?
  1. [math]a_n = -1 + (n-1)*2[/math]
  2. [math]a_n = -1*(2)^(n-1)[/math]
  3. [math]a_1 = -1 ; a_n = a_(n-1) + 2[/math]
  4. [math]a_n = 2 + (n-1)*(-1)[/math]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series
The terms of a sequence differ by the same nonzero number.
  1. Pattern
  2. Common Difference
  3. Arithmetic Sequence
Grade 9 Sequences and Series
1 , 11 , 111 , 1111 ,                 ,                
  1. Arithmetic
  2. Geometric
  3. Neither
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
Which of the following is the explicit formula for the geometric sequence 2, 6, 18, 54, ... ?
  1. [math]a_n=3*2^(n-1)[/math]
  2. [math]a_n=2*3^(n-1)[/math]
  3. [math]a_1=2 ; a_n=3*a_(n-1)[/math]
  4. [math]a_1=3 ; a_n=2*a_(n-1)[/math]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
Which of the following is the recursive formula for the arithmetic sequence 15, 11, 7, 3, ... ?
  1. [math] a_1 = 15 ; a_n = 4^(n-1)[/math]
  2. [math] a_1 = 15 ; a_n = a_(n-1) - 4[/math]
  3. [math]a_1 = 3 ; a_n = a_(n-1) + 4[/math]
  4. [math]a_1 = 3 ; a_n = 15^(n-1)[/math]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series
What type of sequence is the following? [math] 8, 5, 2, -1, ... [/math]
  1. Arithmetic
  2. Geometric
  3. Neither
Grade 9 Sequences and Series CCSS: HSF-IF.A.3
Find the next three terms for the sequence. [math] 14,34,54,74,94,...[/math]
  1. 114, 134, 154
  2. 188, 208, 228
  3. 104, 124, 144
  4. 84, 104, 124
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series CCSS: HSF-BF.A.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]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
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]
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