Flashcards on Linear Sequences and Basic Functions
Linear Sequences & Basic Functions: N Term Rules Explained
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Sequences and nth-term functions
9 cards
Card 1
Question: What is the nth-term rule for the matchstick pattern where the number of matches is double the pattern number plus one more?
Answer: The nth-term rule is 2n + 1.
Card 2
Question: Using the rule 2n + 1, how many matches are needed for the 20th pattern?
Answer: 2 × 20 + 1 = 41 matches.
Card 3
Question: Is 85 a term of the sequence defined by 5n + 8? If not, why?
Answer: No. Solving 5n + 8 = 85 gives n = (85 − 8)/5 = 77/5 = 15.4, which is not a whole number, so 85 is not a term.
Card 4
Question: What is the common difference for the sequence 26, 21, 16, 11, 6?
Answer: The common difference is −5.
Card 5
Question: Given the sequence 26, 21, 16, 11, 6 with common difference −5, what is the general nth-term rule?
Answer: The nth-term rule is 26 + (n−1)(−5) which simplifies to −5n + 31 (presented as +5n+31 in the content appears inconsistent; correct form from sequence
Card 6
Question: What is the common difference listed for the sequence 1, 2, 5, 4, 5, 5, 7 in the content?
Answer: The content lists a common difference of +1.5 (though the sequence shown does not consistently follow a single arithmetic difference).
Card 7
Question: In the input-output mapping X → 2X + 1, what is the corresponding rule for Y?
Answer: Y = 2X + 1.
Card 8
Question: What is the output rule when an input X is mapped by 'X → X4' in the content?
Answer: The content shows examples like 'X → X4' with Y = 4X + 3 in one instance and Y = 3 in another; the mapping is inconsistent in the material.
Card 9
Question: For inputs X = 3,4,5,6,7,8,9,10 and the rule Y = 2X + 1, what would Y be when X = 3?
Answer: Y = 2×3 + 1 = 7.