Practice - Chapter 5: Introduction to Sequences
Practice Questions
Test your understanding with targeted questions
Is the sequence 10, 20, 30, 40, ... created by adding the same number each time? Yes or No.
* Answer: Yes.
* Hint: Look at the difference between consecutive numbers.
💡 Hint: Look at the difference between consecutive numbers.
What is the common difference for the arithmetic sequence 25, 22, 19, 16, ...?
* Answer: -3.
* Hint: Subtract the first term from the second term (22 - 25).
💡 Hint: Subtract the first term from the second term (22 - 25).
7 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the next term in the arithmetic sequence 41, 35, 29, 23, ...?
* Type: mcq
* Options: 19, 18, 17, 16
* Correct Answer: 17
* Explanation: The common difference is -6. Subtracting 6 from the last term (23 - 6) gives 17.
* Hint: Determine the constant number being subtracted to find the pattern.
💡 Hint: Determine the constant number being subtracted to find the pattern.
True or False: The formula an = 10n + 5 represents a geometric sequence.
* Type: boolean
* Options: True, False
* Correct Answer: False
* Explanation: The formula represents a pattern of constant addition (the common difference is 10), which defines an arithmetic sequence (a linear relationship).
* Hint: The variable 'n' is not in the exponent.
💡 Hint: The variable 'n' is not in the exponent.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Investigating Patterns (B): A student is tracking their progress in a video game. Their score sequence is 100, 150, 200, 250, ...
* Task A: Find the formula for the nth term (an) of this sequence.
* Task B: Use the formula to find the term number (n) when the score reaches 500.
* Solution:
* A. Formula: The common difference (d) is 50, and the first term (a1) is 100. Using an = a1 + (n - 1)d, the simplified formula is an = 50n + 50.
* B. Term Number: Set the formula equal to 500: 500 = 50n + 50. Solve for n: 450 = 50n, so n = 9. The score reaches 500 at the 9th term.
* Hint: The formula is the algebraic model; use your equation-solving skills to find 'n'.
💡 Hint: The formula is the algebraic model; use your equation-solving skills to find 'n'.
Communication (C): Explain the difference between the common difference (d) in an arithmetic sequence and the gradient (m) of its corresponding linear graph (from Chapter 6).
* Solution: There is essentially no mathematical difference; they both represent the rate of change.
* Common Difference (d): Describes the vertical change (change in term value) for every step forward in the sequence (change in term position, n).
* Gradient (m): Describes the vertical change (change in y) for every one unit horizontal change (change in x) on the graph.
* Therefore, the common difference (d) is equal to the gradient (m), as both describe the constant rate at which the value increases or decreases.
* Hint: Think about what the gradient represents on a line (rise over run) and what the common difference represents in the sequence. They are the same concept in different forms.
💡 Hint: Think about what the gradient represents on a line (rise over run) and what the common difference represents in the sequence. They are the same concept in different forms.
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