In an arithmetic sequence, a₅ = 28 and a₁₁ = 64. What is its nth term?
Answer and explanation
Correct answer: 6n − 2
The governing concept is the nth-term formula for an arithmetic progression, aₙ = a₁ + (n − 1)d. The difference between the given terms is a₁₁ − a₅ = 64 − 28 = 36. Moving from the fifth term to the eleventh term takes six equal steps, so 6d = 36 and d = 6. Now use a₅ = a₁ + 4d: 28 = a₁ + 24, which gives a₁ = 4. Therefore aₙ = 4 + (n − 1)6 = 4 + 6n − 6 = 6n − 2. Thus option A is correct. Substitution confirms it: at n = 5 the value is 28 and at n = 11 it is 64.
Frequently asked questions
What is the correct answer to this question?
6n − 2
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression, aₙ = a₁ + (n − 1)d. The difference between the given terms is a₁₁ − a₅ = 64 − 28 = 36. Moving from the fifth term to the eleventh term takes six equal steps, so 6d = 36 and d = 6. Now use a₅ = a₁ + 4d: 28 = a₁ + 24, which gives a₁ = 4. Therefore aₙ = 4 + (n − 1)6 = 4 + 6n − 6 = 6n − 2. Thus option A is correct. Substitution confirms it: at n = 5 the value is 28 and at n = 11 it is 64.
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.
