What is the general term of the arithmetic progression (9, 15, 21, 27, …)?
Answer and explanation
Correct answer: aₙ = 6n + 3
The governing concept is the explicit or general rule of an arithmetic progression. The first term is a = 9 and the common difference is d = 15 − 9 = 6. Hence aₙ = a + (n − 1)d = 9 + 6n − 6 = 6n + 3. Substituting n = 1 gives 9, n = 2 gives 15, and n = 3 gives 21, so the rule reproduces the sequence. Therefore, option A is correct. Option B gives 9 for the first term but then increases by 9, not 6. Option C gives 3 as its first term, and option D gives 9 initially but has common difference 3. Checking both the first term and the difference removes these distractors.
Frequently asked questions
What is the correct answer to this question?
aₙ = 6n + 3
Why is this the correct answer?
The governing concept is the explicit or general rule of an arithmetic progression. The first term is a = 9 and the common difference is d = 15 − 9 = 6. Hence aₙ = a + (n − 1)d = 9 + 6n − 6 = 6n + 3. Substituting n = 1 gives 9, n = 2 gives 15, and n = 3 gives 21, so the rule reproduces the sequence. Therefore, option A is correct. Option B gives 9 for the first term but then increases by 9, not 6. Option C gives 3 as its first term, and option D gives 9 initially but has common difference 3. Checking both the first term and the difference removes these 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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