Flashcards on Linear Sequences and Basic Functions

Linear Sequences & Basic Functions: N Term Rules Explained

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What is the nth-term rule for the matchstick pattern where the number of matches is double the pattern number plus one more?

The nth-term rule is 2n + 1.

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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.