What is the general term of the sequence (4, 8, 12, 16, …)?
Answer and explanation
Correct answer: a_n = 4n
The sequence is formed by consecutive multiples of 4. The first term is 4 × 1, the second is 4 × 2, the third is 4 × 3, and the fourth is 4 × 4. Therefore the explicit general term is a_n = 4n, which makes option A correct. Using the arithmetic formula gives the same result: a_1 = 4 and d = 4, so a_n = 4 + (n − 1)4 = 4n. Substitution confirms that n = 1, 2, 3, and 4 produce 4, 8, 12, and 16. Option B has common difference 1, option C gives 4, 7, 10, …, and option D gives 3 as its first term. Hence only option A matches both the starting value and the constant difference.
Frequently asked questions
What is the correct answer to this question?
a_n = 4n
Why is this the correct answer?
The sequence is formed by consecutive multiples of 4. The first term is 4 × 1, the second is 4 × 2, the third is 4 × 3, and the fourth is 4 × 4. Therefore the explicit general term is a_n = 4n, which makes option A correct. Using the arithmetic formula gives the same result: a_1 = 4 and d = 4, so a_n = 4 + (n − 1)4 = 4n. Substitution confirms that n = 1, 2, 3, and 4 produce 4, 8, 12, and 16. Option B has common difference 1, option C gives 4, 7, 10, …, and option D gives 3 as its first term. Hence only option A matches both the starting value and the constant difference.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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