In an arithmetic sequence, a₆ = 47 and a₁₃ = 110. What is its nth term?
Answer and explanation
Correct answer: 9n − 7
For an arithmetic progression, the difference between terms equals the number of steps multiplied by the common difference. From a₁₃ − a₆ = (13 − 6)d, we obtain 110 − 47 = 7d, so 63 = 7d and d = 9. Now use a₆ = a₁ + 5d: 47 = a₁ + 45, giving a₁ = 2. Hence aₙ = a₁ + (n − 1)d = 2 + 9(n − 1) = 9n − 7, so option B is correct. Checking gives a₆ = 54 − 7 = 47 and a₁₃ = 117 − 7 = 110. The other options fail one or both checks.
Frequently asked questions
What is the correct answer to this question?
9n − 7
Why is this the correct answer?
For an arithmetic progression, the difference between terms equals the number of steps multiplied by the common difference. From a₁₃ − a₆ = (13 − 6)d, we obtain 110 − 47 = 7d, so 63 = 7d and d = 9. Now use a₆ = a₁ + 5d: 47 = a₁ + 45, giving a₁ = 2. Hence aₙ = a₁ + (n − 1)d = 2 + 9(n − 1) = 9n − 7, so option B is correct. Checking gives a₆ = 54 − 7 = 47 and a₁₃ = 117 − 7 = 110. The other options fail one or both checks.
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.
