What is the 30th term of the sequence 12, 19, 26, 33, …?
Answer and explanation
Correct answer: 215
The governing concept is the nth-term formula of an arithmetic sequence. Consecutive terms increase by 7, so the sequence has first term a₁ = 12 and common difference d = 7. Its explicit rule is aₙ = a₁ + (n − 1)d = 12 + 7(n − 1) = 7n + 5. Substituting n = 30 gives a₃₀ = 7(30) + 5 = 210 + 5 = 215. Therefore option B is correct. Option A is 7 less than the correct result and would come from using 29 without the required first-term adjustment; C and D are obtained by adding too much. The explicit formula avoids listing all thirty terms and is the efficient method.
Frequently asked questions
What is the correct answer to this question?
215
Why is this the correct answer?
The governing concept is the nth-term formula of an arithmetic sequence. Consecutive terms increase by 7, so the sequence has first term a₁ = 12 and common difference d = 7. Its explicit rule is aₙ = a₁ + (n − 1)d = 12 + 7(n − 1) = 7n + 5. Substituting n = 30 gives a₃₀ = 7(30) + 5 = 210 + 5 = 215. Therefore option B is correct. Option A is 7 less than the correct result and would come from using 29 without the required first-term adjustment; C and D are obtained by adding too much. The explicit formula avoids listing all thirty terms and is the efficient method.
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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