What is the general term of the arithmetic progression (12, 20, 28, 36, ...)?
Answer and explanation
Correct answer: a_n = 8n + 4
The governing concept is the nth-term formula for an arithmetic progression: a_n = a_1 + (n - 1)d. Here the first term is a_1 = 12, and the common difference is d = 20 - 12 = 8; the same difference appears between every consecutive pair. Substituting these values gives a_n = 12 + (n - 1)8 = 12 + 8n - 8 = 8n + 4. Therefore option A is correct. A quick check confirms it: for n = 1, the formula gives 12; for n = 2 it gives 20; and for n = 4 it gives 36. Option C gives 4 at n = 1, option B gives 12n, and option D gives 12 at n = 1 but fails at later terms.
Frequently asked questions
What is the correct answer to this question?
a_n = 8n + 4
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: a_n = a_1 + (n - 1)d. Here the first term is a_1 = 12, and the common difference is d = 20 - 12 = 8; the same difference appears between every consecutive pair. Substituting these values gives a_n = 12 + (n - 1)8 = 12 + 8n - 8 = 8n + 4. Therefore option A is correct. A quick check confirms it: for n = 1, the formula gives 12; for n = 2 it gives 20; and for n = 4 it gives 36. Option C gives 4 at n = 1, option B gives 12n, and option D gives 12 at n = 1 but fails at later terms.
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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