If a₂ = 12 and d = 9, what is the 7th term?
Answer and explanation
Correct answer: 57
The governing concept is finding a term of an arithmetic progression from another known term. Instead of restarting from the first term, use aₙ = aᵣ + (n − r)d. Here the known term is a₂ = 12, the required term is a₇, and d = 9. The number of equal steps from the second position to the seventh position is 7 − 2 = 5, not 7. Therefore a₇ = 12 + (7 − 2)×9 = 12 + 5×9 = 12 + 45 = 57. Hence option B is correct. The distractors can result from adding the common difference the wrong number of times or from a simple arithmetic error. Counting gaps between positions prevents that mistake.
Frequently asked questions
What is the correct answer to this question?
57
Why is this the correct answer?
The governing concept is finding a term of an arithmetic progression from another known term. Instead of restarting from the first term, use aₙ = aᵣ + (n − r)d. Here the known term is a₂ = 12, the required term is a₇, and d = 9. The number of equal steps from the second position to the seventh position is 7 − 2 = 5, not 7. Therefore a₇ = 12 + (7 − 2)×9 = 12 + 5×9 = 12 + 45 = 57. Hence option B is correct. The distractors can result from adding the common difference the wrong number of times or from a simple arithmetic error. Counting gaps between positions prevents that mistake.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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