If aₙ = 8n − 5, which term is equal to 155?
Answer and explanation
Correct answer: n = 20
The governing concept is using an explicit sequence rule to identify the position of a specified term. Set the nth-term expression equal to the given value: 8n − 5 = 155. Adding 5 to both sides gives 8n = 160, and dividing by 8 gives n = 20. A check confirms that a₂₀ = 8(20) − 5 = 160 − 5 = 155. Hence option C is correct. Option A would produce 139, option B would produce 147, and option D would produce 163. These distractors result from choosing a nearby position or making an arithmetic error, but none satisfies the defining equation.
Frequently asked questions
What is the correct answer to this question?
n = 20
Why is this the correct answer?
The governing concept is using an explicit sequence rule to identify the position of a specified term. Set the nth-term expression equal to the given value: 8n − 5 = 155. Adding 5 to both sides gives 8n = 160, and dividing by 8 gives n = 20. A check confirms that a₂₀ = 8(20) − 5 = 160 − 5 = 155. Hence option C is correct. Option A would produce 139, option B would produce 147, and option D would produce 163. These distractors result from choosing a nearby position or making an arithmetic error, but none satisfies the defining equation.
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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