What is the nth term of the sequence (5, 9, 13, 17, ...)?
Answer and explanation
Correct answer: aₙ = 4n + 1
The sequence is an arithmetic progression with first term 5 and common difference 4, since 9 − 5 = 4, 13 − 9 = 4, and 17 − 13 = 4. Apply aₙ = a₁ + (n − 1)d: aₙ = 5 + (n − 1)4 = 5 + 4n − 4 = 4n + 1. Thus option A is the correct general rule. The first-term check is decisive: for n = 1, 4(1) + 1 = 5; for n = 2, the value is 9; for n = 3, it is 13. Option C starts at 3, option D starts at 5 but then increases by only 1, and option B starts at 4, so these do not generate the full sequence.
Frequently asked questions
What is the correct answer to this question?
aₙ = 4n + 1
Why is this the correct answer?
The sequence is an arithmetic progression with first term 5 and common difference 4, since 9 − 5 = 4, 13 − 9 = 4, and 17 − 13 = 4. Apply aₙ = a₁ + (n − 1)d: aₙ = 5 + (n − 1)4 = 5 + 4n − 4 = 4n + 1. Thus option A is the correct general rule. The first-term check is decisive: for n = 1, 4(1) + 1 = 5; for n = 2, the value is 9; for n = 3, it is 13. Option C starts at 3, option D starts at 5 but then increases by only 1, and option B starts at 4, so these do not generate the full sequence.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
