What is the nth term of the sequence (4, 10, 16, 22, ...)?
Answer and explanation
Correct answer: aₙ = 6n − 2
This is an arithmetic progression because the difference between consecutive terms is always 6: 10 − 4 = 6, 16 − 10 = 6, and 22 − 16 = 6. The nth-term formula is aₙ = a₁ + (n − 1)d. Using a₁ = 4 and d = 6 gives aₙ = 4 + (n − 1)6 = 4 + 6n − 6 = 6n − 2. Thus option A is correct. Testing the formula produces 4 when n = 1, 10 when n = 2, 16 when n = 3, and 22 when n = 4. Option B starts at 8, option C starts at 10, and option D has common difference 2. These alternatives cannot represent the given progression.
Frequently asked questions
What is the correct answer to this question?
aₙ = 6n − 2
Why is this the correct answer?
This is an arithmetic progression because the difference between consecutive terms is always 6: 10 − 4 = 6, 16 − 10 = 6, and 22 − 16 = 6. The nth-term formula is aₙ = a₁ + (n − 1)d. Using a₁ = 4 and d = 6 gives aₙ = 4 + (n − 1)6 = 4 + 6n − 6 = 6n − 2. Thus option A is correct. Testing the formula produces 4 when n = 1, 10 when n = 2, 16 when n = 3, and 22 when n = 4. Option B starts at 8, option C starts at 10, and option D has common difference 2. These alternatives cannot represent the given progression.
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.
