Which general term is correct for the sequence 2, 23, 124, 625, …?
Answer and explanation
Correct answer: aₙ = 5ⁿ + n − 4
The governing concept is an explicit rule containing exponential growth. Substitute the position n into option A: for n = 1, 5¹ + 1 − 4 = 2; for n = 2, 5² + 2 − 4 = 23; for n = 3, 5³ + 3 − 4 = 124; and for n = 4, 5⁴ + 4 − 4 = 625. Thus the formula exactly generates the four given terms, so A is correct. Option B is linear and gives 7 for the first term, option C gives 7 for the first term, and option D gives −3 for n = 1 and 28 for n = 2. The small adjustment n − 4 must not be omitted when checking the power pattern.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5ⁿ + n − 4
Why is this the correct answer?
The governing concept is an explicit rule containing exponential growth. Substitute the position n into option A: for n = 1, 5¹ + 1 − 4 = 2; for n = 2, 5² + 2 − 4 = 23; for n = 3, 5³ + 3 − 4 = 124; and for n = 4, 5⁴ + 4 − 4 = 625. Thus the formula exactly generates the four given terms, so A is correct. Option B is linear and gives 7 for the first term, option C gives 7 for the first term, and option D gives −3 for n = 1 and 28 for n = 2. The small adjustment n − 4 must not be omitted when checking the power pattern.
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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