If aₙ = (3n + 2)/(2n − 1), what is a₃?
Answer and explanation
Correct answer: 11/5
The governing concept is direct substitution into an explicit fractional rule. To find a₃, replace every occurrence of n by 3, not just the n in the numerator. Thus a₃ = [3(3) + 2]/[2(3) − 1] = (9 + 2)/(6 − 1) = 11/5. Therefore option C is correct. Option A results from reducing the numerator incorrectly, option B omits the added 2 in the numerator, and option D uses an incorrect numerator value. The denominator must also be evaluated carefully; it is 5, not 6, because the expression is 2n − 1. Since 11 and 5 have no common factor, 11/5 is already in simplest form.
Frequently asked questions
What is the correct answer to this question?
11/5
Why is this the correct answer?
The governing concept is direct substitution into an explicit fractional rule. To find a₃, replace every occurrence of n by 3, not just the n in the numerator. Thus a₃ = [3(3) + 2]/[2(3) − 1] = (9 + 2)/(6 − 1) = 11/5. Therefore option C is correct. Option A results from reducing the numerator incorrectly, option B omits the added 2 in the numerator, and option D uses an incorrect numerator value. The denominator must also be evaluated carefully; it is 5, not 6, because the expression is 2n − 1. Since 11 and 5 have no common factor, 11/5 is already in simplest form.
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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