What is the (n)th term of the sequence (4,16,36,64,\ldots)?

Correct answer: (4n^2)

The sequence is 4, 16, 36, 64, and each term can be viewed as four times a square. The first term is \\(4\\times1^2\\), the second is \\(4\\times2^2\\), the third is \\(4\\times3^2\\), and the fourth is \\(4\\times4^2\\). Thus the number inside the square is exactly the position number. Recognizing this structure is more reliable than guessing from differences alone.

For the nth position, replace the position number by \\(n\\). The general term is therefore \\(a_n=4n^2\\). Checking it confirms the pattern: \\(4(1)^2=4\\), \\(4(2)^2=16\\), \\(4(3)^2=36\\), and \\(4(4)^2=64\\). Hence option A is correct. Option B gives half the required values, while the linear expression in option C cannot produce this square-based growth.