Froggy Jump: Sequences Quest

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Arithmetic & Geometric race

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Dennis Bico

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Froggy Jumps Froggy Jump: Sequences QuestVersión en línea Arithmetic & Geometric race por Dennis Bico 1 1. Which sequence type has a constant difference between consecutive terms? a Geometric b Fibonacci c Arithmetic 2 2. What is the common ratio of 4, 12, 36, 108, …? a 3 b 2 c 4 3 3. Which formula gives the nth term of a geometric sequence? a a_n = a_1 · r^n b a_n = a_1 · r^(n-1) c a_n = a_1 + (n-1)d 4 4. What is the arithmetic mean between 12 and 20? a 16 b 14 c 18 5 5. Which sequence has reciprocals forming an arithmetic sequence? a Harmonic b Geometric c Arithmetic 6 6. Which option is a geometric sequence? a 2, 4, 6, 8 b 5, 10, 20, 40 c 1, 3, 5, 7 7 7. For an infinite geometric series, when does it converge to a finite sum? a \|r\| < 1 b r = 1 c r > 1 8 8. Which formula gives the sum to infinity of a geometric series? a S∞ = a1 / (1 − r) b S∞ = a1(1 − r) c S∞ = a1 / (1 + r) 9 9. A sequence starts at 5 and ends at 25 with one mean. Which sequence is correct? a 5, 10, 25 b 5, 20, 25 c 5, 15, 25 10 10. Which statement best defines a mathematical sequence? a A list with no rule b A set of numbers following a logical, repeatable rule. c A random group of numbers

Froggy Jumps

Froggy Jump: Sequences QuestVersión en línea

Arithmetic & Geometric race

por Dennis Bico

1. Which sequence type has a constant difference between consecutive terms?

Geometric

Fibonacci

Arithmetic

2. What is the common ratio of 4, 12, 36, 108, …?

3. Which formula gives the nth term of a geometric sequence?

a_n = a_1 · r^n

a_n = a_1 · r^(n-1)

a_n = a_1 + (n-1)d

4. What is the arithmetic mean between 12 and 20?

5. Which sequence has reciprocals forming an arithmetic sequence?

Harmonic

Geometric

Arithmetic

6. Which option is a geometric sequence?

2, 4, 6, 8

5, 10, 20, 40

1, 3, 5, 7

7. For an infinite geometric series, when does it converge to a finite sum?

|r| < 1

r = 1

r > 1

8. Which formula gives the sum to infinity of a geometric series?

S∞ = a1 / (1 − r)

S∞ = a1(1 − r)

S∞ = a1 / (1 + r)

9. A sequence starts at 5 and ends at 25 with one mean. Which sequence is correct?

5, 10, 25

5, 20, 25

5, 15, 25

10. Which statement best defines a mathematical sequence?

A list with no rule

A set of numbers following a logical, repeatable rule.

A random group of numbers

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Froggy Jump: Sequences Quest

Froggy Jumps

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Creada por

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Froggy Jump: Sequences QuestVersión en línea

por Dennis Bico

1. Which sequence type has a constant difference between consecutive terms?

2. What is the common ratio of 4, 12, 36, 108, …?

3. Which formula gives the nth term of a geometric sequence?

4. What is the arithmetic mean between 12 and 20?

5. Which sequence has reciprocals forming an arithmetic sequence?

6. Which option is a geometric sequence?

7. For an infinite geometric series, when does it converge to a finite sum?

8. Which formula gives the sum to infinity of a geometric series?

9. A sequence starts at 5 and ends at 25 with one mean. Which sequence is correct?

10. Which statement best defines a mathematical sequence?

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