If aₙ = 8n − 3, at which term will aₙ = 77?
Answer and explanation
Correct answer: 10th
The governing concept is finding the index of a specified term from a linear explicit rule. Set the expression equal to the required value: 8n − 3 = 77. Adding 3 to both sides gives 8n = 80, and dividing by 8 gives n = 10. Therefore 77 occurs at the tenth term, so option B is correct. Substitution confirms the result: a₁₀ = 8(10) − 3 = 80 − 3 = 77. The distractors correspond to nearby indices, but they give different values: a₉ = 69, a₁₁ = 85, and a₁₂ = 93. The essential distinction is between the term value, 77, and its position, n = 10. Writing the equation before solving prevents confusion and ensures that the index is obtained rather than another sequence value.
Frequently asked questions
What is the correct answer to this question?
10th
Why is this the correct answer?
The governing concept is finding the index of a specified term from a linear explicit rule. Set the expression equal to the required value: 8n − 3 = 77. Adding 3 to both sides gives 8n = 80, and dividing by 8 gives n = 10. Therefore 77 occurs at the tenth term, so option B is correct. Substitution confirms the result: a₁₀ = 8(10) − 3 = 80 − 3 = 77. The distractors correspond to nearby indices, but they give different values: a₉ = 69, a₁₁ = 85, and a₁₂ = 93. The essential distinction is between the term value, 77, and its position, n = 10. Writing the equation before solving prevents confusion and ensures that the index is obtained rather than another sequence value.
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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