If aₙ = n² + qn + 4 and a₅ = 54, what is the value of q?
Answer and explanation
Correct answer: 5
Because the fifth term is known, substitute n = 5 into the explicit formula. We obtain a₅ = 5² + 5q + 4 = 25 + 5q + 4 = 29 + 5q. Equating this to 54 gives 29 + 5q = 54, so 5q = 25 and q = 5. Hence option C is correct. The other choices arise from an incorrect substitution of 5 or from mishandling the constant term.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Because the fifth term is known, substitute n = 5 into the explicit formula. We obtain a₅ = 5² + 5q + 4 = 25 + 5q + 4 = 29 + 5q. Equating this to 54 gives 29 + 5q = 54, so 5q = 25 and q = 5. Hence option C is correct. The other choices arise from an incorrect substitution of 5 or from mishandling the constant term.
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.
