What is the (n)th term of the sequence (9,16,25,36,49,\ldots)?
Answer and explanation
Correct answer: \((n+2)^2\)
The given terms are \(3^2,4^2,5^2,6^2,7^2\), respectively. For term number \(n=1\), the base of the square is \(3\), so the base follows the pattern \(n+2\). Hence, the nth term is \((n+2)^2\). For example, at \(n=2\), it gives \((2+2)^2=16\). The expression \(n^2+8\) gives 12 for the second term, so it is not correct. Exam tip: write the initial terms as perfect squares and observe the sequence of their square roots.
Frequently asked questions
What is the correct answer to this question?
\((n+2)^2\)
Why is this the correct answer?
The given terms are \(3^2,4^2,5^2,6^2,7^2\), respectively. For term number \(n=1\), the base of the square is \(3\), so the base follows the pattern \(n+2\). Hence, the nth term is \((n+2)^2\). For example, at \(n=2\), it gives \((2+2)^2=16\). The expression \(n^2+8\) gives 12 for the second term, so it is not correct. Exam tip: write the initial terms as perfect squares and observe the sequence of their square roots.
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.
