What is the general term of the sequence (3, 8, 13, 18, …)?
Answer and explanation
Correct answer: aₙ = 5n − 2
The sequence increases by a constant difference of 5, so it is an arithmetic sequence. For an arithmetic sequence, the nth term is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. Here a₁ = 3 and d = 5, so aₙ = 3 + (n − 1)5 = 3 + 5n − 5 = 5n − 2. Thus option A is correct. Checking confirms the result: for n = 1, 5(1) − 2 = 3; for n = 2, the value is 8; for n = 3, it is 13; and for n = 4, it is 18. The other formulas fail at one or more of these positions.
Frequently asked questions
What is the correct answer to this question?
aₙ = 5n − 2
Why is this the correct answer?
The sequence increases by a constant difference of 5, so it is an arithmetic sequence. For an arithmetic sequence, the nth term is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. Here a₁ = 3 and d = 5, so aₙ = 3 + (n − 1)5 = 3 + 5n − 5 = 5n − 2. Thus option A is correct. Checking confirms the result: for n = 1, 5(1) − 2 = 3; for n = 2, the value is 8; for n = 3, it is 13; and for n = 4, it is 18. The other formulas fail at one or more of these positions.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
