In the sequence (3, 6, 9, 12, ...), which term is 36?
Answer and explanation
Correct answer: Twelfth term
The governing concept is finding the position of a given value by using the general term. This is an arithmetic sequence with first term 3 and common difference 3, so its nth term is aₙ=3n. To find the position of 36, set 3n=36 and divide both sides by 3: n=12. Hence 36 is the twelfth term, so option C is correct. Direct listing also confirms it: the kth multiple of 3 is 3k, and 36=3×12. Option A gives 3×10=30, option B gives 3×11=33, and option D gives 3×13=39. Those values lie near 36 but do not equal it, so they are plausible counting distractors.
Frequently asked questions
What is the correct answer to this question?
Twelfth term
Why is this the correct answer?
The governing concept is finding the position of a given value by using the general term. This is an arithmetic sequence with first term 3 and common difference 3, so its nth term is aₙ=3n. To find the position of 36, set 3n=36 and divide both sides by 3: n=12. Hence 36 is the twelfth term, so option C is correct. Direct listing also confirms it: the kth multiple of 3 is 3k, and 36=3×12. Option A gives 3×10=30, option B gives 3×11=33, and option D gives 3×13=39. Those values lie near 36 but do not equal it, so they are plausible counting distractors.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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