Which general term is correct for the sequence (9, 14, 19, 24, …)?
Answer and explanation
Correct answer: a_n = 5n + 4
The sequence has a constant difference, so the arithmetic-sequence formula applies. The common difference is d = 14 − 9 = 5. Therefore a_n = a_1 + (n − 1)d = 9 + (n − 1)5 = 9 + 5n − 5 = 5n + 4. Thus option A is correct. Testing the first positions gives a_1 = 5 + 4 = 9, a_2 = 10 + 4 = 14, a_3 = 15 + 4 = 19, and a_4 = 20 + 4 = 24. Option B gives 9, 18, 27, …; option C gives 1 as its first term; and option D gives 9, 10, 11, …. The constant part must be 4, not 0, −4, or 8, in order to fit the first term and the difference.
Frequently asked questions
What is the correct answer to this question?
a_n = 5n + 4
Why is this the correct answer?
The sequence has a constant difference, so the arithmetic-sequence formula applies. The common difference is d = 14 − 9 = 5. Therefore a_n = a_1 + (n − 1)d = 9 + (n − 1)5 = 9 + 5n − 5 = 5n + 4. Thus option A is correct. Testing the first positions gives a_1 = 5 + 4 = 9, a_2 = 10 + 4 = 14, a_3 = 15 + 4 = 19, and a_4 = 20 + 4 = 24. Option B gives 9, 18, 27, …; option C gives 1 as its first term; and option D gives 9, 10, 11, …. The constant part must be 4, not 0, −4, or 8, in order to fit the first term and the 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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