Which is the (n)th term of the sequence (5,11,19,29,41,\ldots)?
Answer and explanation
Correct answer: (n^2+3n+1)
The successive differences are 6, 8, 10, and 12, so the second difference is constantly 2. This indicates a quadratic expression with leading coefficient 1, so write the term as \(a_n=n^2+bn+c\). Use the first two terms. For n=1, \(1+b+c=5\), giving \(b+c=4\). For n=2, \(4+2b+c=11\), giving \(2b+c=7\). Subtracting gives \(b=3\), and then \(c=1\).
Thus \(a_n=n^2+3n+1\), which is option B. A quick check gives 5 for n=1, 11 for n=2, and 19 for n=3. The constant second difference confirms the quadratic form, while direct substitution determines the remaining coefficients. The supplied answer and explanation are accurate.
Frequently asked questions
What is the correct answer to this question?
(n^2+3n+1)
Why is this the correct answer?
The successive differences are 6, 8, 10, and 12, so the second difference is constantly 2. This indicates a quadratic expression with leading coefficient 1, so write the term as \(a_n=n^2+bn+c\). Use the first two terms. For n=1, \(1+b+c=5\), giving \(b+c=4\). For n=2, \(4+2b+c=11\), giving \(2b+c=7\). Subtracting gives \(b=3\), and then \(c=1\).
Thus \(a_n=n^2+3n+1\), which is option B. A quick check gives 5 for n=1, 11 for n=2, and 19 for n=3. The constant second difference confirms the quadratic form, while direct substitution determines the remaining coefficients. The supplied answer and explanation are accurate.
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.
