Which explicit rule is correct for the sequence (1, 7, 25, 79, …)?
Answer and explanation
Correct answer: aₙ = 3ⁿ − 2
The sequence follows powers of 3 with 2 subtracted from each term. Evaluating the proposed rule aₙ = 3ⁿ − 2 gives, for n = 1, 3 − 2 = 1; for n = 2, 9 − 2 = 7; for n = 3, 27 − 2 = 25; and for n = 4, 81 − 2 = 79. Hence option B is correct. Option A gives 3, 9, 27, 81 because it omits the subtraction of 2. Option C gives 1, 3, 7, 15, and option D gives 0, 7, 26, 63, so neither agrees with the sequence. The key concept is an explicit exponential rule: the position determines the exponent, and the fixed adjustment is then applied.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3ⁿ − 2
Why is this the correct answer?
The sequence follows powers of 3 with 2 subtracted from each term. Evaluating the proposed rule aₙ = 3ⁿ − 2 gives, for n = 1, 3 − 2 = 1; for n = 2, 9 − 2 = 7; for n = 3, 27 − 2 = 25; and for n = 4, 81 − 2 = 79. Hence option B is correct. Option A gives 3, 9, 27, 81 because it omits the subtraction of 2. Option C gives 1, 3, 7, 15, and option D gives 0, 7, 26, 63, so neither agrees with the sequence. The key concept is an explicit exponential rule: the position determines the exponent, and the fixed adjustment is then applied.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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