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Sequences and Series Questions - All Grades

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Grade 10 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2
What is the explicit function of the geometric sequence 3, 4.5, 6.75, ...?
  1. [math]f(n)=1.5f(n-1)[/math] where [math]f(1)=3[/math]
  2. [math]f(n)=3*1.5^(n-1)[/math]
  3. [math]f(n)=1.5*3^(n-1)[/math]
  4. [math]f(n)=3f(n-1)[/math] where [math]f(1)=1.5[/math]
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 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Given the sequence [math]1,4,16,64,256,...[/math], which of the following correctly defines this sequence in a recursive form? Assume that [math]n in NN[/math].
  1. [math]t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1[/math]
  2. [math]t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1[/math]
  3. [math]t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1[/math]
  4. [math]t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1[/math]
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4
Find the sum of the finite geometric series.
[math]1+4+16+64 +...+4^9[/math]
  1. [math]516[/math]
  2. [math]2","073.3[/math]
  3. [math]25","347[/math]
  4. [math]349","525[/math]
  5. None of these are correct
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
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
What are the next 2 numbers in the sequence [math]1, 5, 9...[/math]?
  1. [math]45,225[/math]
  2. [math]14,18[/math]
  3. [math]13,17[/math]
  4. [math]32,128[/math]
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_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 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 10 Sequences and Series CCSS: HSF-IF.A.3
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]
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