What is the general term of the sequence 4, 36, 100, 196, …?
Answer and explanation
Correct answer: aₙ = (4n − 2)²
The governing concept is deriving a general term from a pattern of perfect squares. Rewrite the sequence as 2², 6², 10², and 14². The bases form an arithmetic sequence beginning at 2 and increasing by 4, so the nth base is 2 + (n − 1)4 = 4n − 2. Squaring this base gives aₙ = (4n − 2)². Substitution confirms the result: n = 1 gives 2² = 4, n = 2 gives 6² = 36, n = 3 gives 10² = 100, and n = 4 gives 14² = 196. Option A produces 4, 16, 36, 64; C starts with 16; and D is not consistent. Hence B is correct.
Frequently asked questions
What is the correct answer to this question?
aₙ = (4n − 2)²
Why is this the correct answer?
The governing concept is deriving a general term from a pattern of perfect squares. Rewrite the sequence as 2², 6², 10², and 14². The bases form an arithmetic sequence beginning at 2 and increasing by 4, so the nth base is 2 + (n − 1)4 = 4n − 2. Squaring this base gives aₙ = (4n − 2)². Substitution confirms the result: n = 1 gives 2² = 4, n = 2 gives 6² = 36, n = 3 gives 10² = 100, and n = 4 gives 14² = 196. Option A produces 4, 16, 36, 64; C starts with 16; and D is not consistent. Hence B is correct.
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.
