Which rule is correct for the sequence (7, 11, 15, 19, …)?
Answer and explanation
Correct answer: a_n = 4n + 3
The sequence follows an explicit arithmetic rule. Its common difference is 11 − 7 = 4, so the coefficient of n in the general term is 4. Applying a_n = a_1 + (n − 1)d gives a_n = 7 + (n − 1)4 = 7 + 4n − 4 = 4n + 3. Therefore option A is correct. Substitution confirms that n = 1 gives 7, n = 2 gives 11, n = 3 gives 15, and n = 4 gives 19. Option B gives 7, 14, 21, …; option C starts with 1; and option D gives 7, 8, 9, …. These alternatives either use the wrong difference or fail to preserve the pattern, so they cannot be the required general rule.
Frequently asked questions
What is the correct answer to this question?
a_n = 4n + 3
Why is this the correct answer?
The sequence follows an explicit arithmetic rule. Its common difference is 11 − 7 = 4, so the coefficient of n in the general term is 4. Applying a_n = a_1 + (n − 1)d gives a_n = 7 + (n − 1)4 = 7 + 4n − 4 = 4n + 3. Therefore option A is correct. Substitution confirms that n = 1 gives 7, n = 2 gives 11, n = 3 gives 15, and n = 4 gives 19. Option B gives 7, 14, 21, …; option C starts with 1; and option D gives 7, 8, 9, …. These alternatives either use the wrong difference or fail to preserve the pattern, so they cannot be the required general rule.
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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