Questions and Answers
What is the explicit formula for g(n) given g(n) = 2.7 x 6.1^(n-1)?
g(n) = 2.7 x 6.1^(n-1)
Who has the correct formula for the sequence 80, 40, 20, 10,...?
Which of the following formulas is correct for the sequence 4, 12, 36, 108,...?
Complete the recursive formula of the geometric sequence -0.56, -5.6, -5, -560,... a) c(1) = ____ b) c(n) = c(n-1) x _____
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What is the explicit formula for g(n) if g(n) = 2.7 x 6.1^(n-1)?
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Who is right about the formula for the sequence 80, 40, 20, 10,...?
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Who is right about the formula for the sequence 4, 12, 36, 108,...?
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Complete the recursive formula of the geometric sequence -0.56, -5.6, -5, -560: c(1) = _____ and c(n) = c(n-1) x _____
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Complete the recursive formula of the geometric sequence 27, -9, 3, -1: b(1) = _____ and b(n) = b(n-1) x _____
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What is the explicit formula for the geometric sequence -8, -40, -200, -1000?
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Complete the recursive formula of h(n) = -13n: h(1) = _____ and h(n) = h(n-1) + _____
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What is the least possible number of times that Miranda has been to the store, if each time she spends $7 and Savannah spends $9?
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How many days until Camryn practices the trumpet and flute again on the same day?
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If Rafaela has 25 girls and 35 boys and wants to create the greatest number of equal teams, how many boys will be on each team?
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What is the greatest number of packages Tim can make with 39 pairs of headphones and 13 music players?
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What is the greatest number of identical snack bags that Destiny can make from 18 chocolate bars and 12 cookies?
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What is the least number of total pins Sam and Carlos could have knocked down together?
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Study Notes
Geometric Sequences
- g(n) = 2.7 x 6.1^(n-1) is an explicit formula for a geometric sequence with g(1) = 2.7 and recursive relation g(n) = g(n - 1) x 6.1.
Explicit Formulas from Two Perspectives
- Divya's formula h(n) = 80 x (1/2)^(n-1) simplifies to Miguel's h(n) = 160 x (1/2)^n, making Miguel’s formula correct for the sequence 80, 40, 20, 10.
- For the sequence 4, 12, 36, 108, the correct explicit formula is g(n) = 4 x 3^(n-1), contradicting both Haruka and Mustafa's formulas.
Completing Recursive Formulas
- For -0.56, -5.6, -5, -560, c(1) = -0.56; c(n) = c(n-1) x 10.
- For 27, -9, 3, -1, b(1) = 27; b(n) = b(n-1) x (-1/3).
- The explicit formula for the sequence -8, -40, -200, -1000 is c(n) = -8 x 5^(n-1).
Linear Sequences
- The recursive relationship for h(n) = -13n is defined by h(1) = -13 and h(n) = h(n-1) - 13.
Problem-Solving Scenarios
- Miranda and Savannah, spending $7 and $9 respectively, can have equal expenditure after a minimum of 9 shopping trips for Miranda.
- Camryn practices trumpet every 11 days and flute every 3 days; the next shared practice will be after 33 days.
- Rafaela has 25 girls and 35 boys; with the largest possible teams, each team would have 7 boys due to the GCF of 35 and 25.
- Tim can create 13 identical packages if he uses all 39 headphones and 13 music players. The greatest arrangement of students in equal rows from 72 boys and 90 girls totals to 18 students per row.
Identical Snack Bags
- Destiny can create 6 identical snack bags from 18 chocolate bars and 12 cookies, determined by the GCF of the quantities.
- Sam and Carlos each knocking down 72 total pins (8 pins per bowl for Sam and 9 for Carlos) concludes the least number of pins knocked down equitably.
Guard Problem
- In a specific scenario with guards, dividing 80 by the GCF of 16 results in 5 guards per team.
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Description
Test your knowledge on geometric and linear sequences with this quiz. It covers explicit and recursive formulas, including problem-solving scenarios related to sequences. Challenge yourself with different examples and verify your understanding of these mathematical concepts.
