Flashcards on Introduction to Numerical Sequences
Introduction to Numerical Sequences: Rules & Examples
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Mathematics sequences
9 cards
Card 1
Question: What is a term-to-term rule for the sequence 7, 10½, 14, 17½?
Answer: Add 3½ to get the next term (term-to-term rule: +3½).
Card 2
Question: Using the term-to-term rule +3½, what are the next two terms after 17½?
Answer: 21 and 24½ (17½ + 3½ = 21; 21 + 3½ = 24½).
Card 3
Question: What is the term-to-term rule for the sequence 10, 9.8, 9.6, 9.4?
Answer: Subtract 0.2 each time (term-to-term rule: −0.2).
Card 4
Question: Using the term-to-term rule −0.2, what are the next two terms after 9.4?
Answer: 9.2 and 9.0 (9.4 − 0.2 = 9.2; 9.2 − 0.2 = 9.0).
Card 5
Question: How do you express a position-to-term rule algebraically when the nth term is 3n + 1?
Answer: Write the nth term as 3n + 1, where n is the position number.
Card 6
Question: Given the table: positions 1,2,3,4 produce terms 4,7,10,13 — what position-to-term rule fits this sequence?
Answer: Term = 3n + 1 (each term increases by 3; at n=1 gives 4).
Card 7
Question: Find a position-to-term rule for the decreasing sequence 18,16,14,12,10 ...
Answer: Term = −2n + 20 (multiply position n by −2 then add 20).
Card 8
Question: Using the rule Term = −2n + 20, what is the 6th and 21st term?
Answer: 6th term = −2(6)+20 = 8; 21st term = −2(21)+20 = −22.
Card 9
Question: What is the difference between a term-to-term rule and a position-to-term rule?
Answer: Term-to-term rule gives the operation to get from one term to the next (e.g., +3½); position-to-term rule gives a formula for the nth term in terms of