In the sequence (1,4,9,16,25,\ldots), which term is (196)?

(14)th

The sequence is formed by squaring the positive counting numbers: the first term is 1 squared, the second is 2 squared, the third is 3 squared, and so on. Thus its general term is \\(a_n=n^2\\). To find the position of 196, solve \\(n^2=196\\). Since \\(14^2=196\\) and the term number is positive, \\(n=14\\). Therefore, 196 is the 14th term, so option A is correct. The other listed positions would produce different squares.

The pattern can also be checked directly: the terms are 1, 4, 9, 16, 25, ..., which are the squares of 1, 2, 3, 4, 5, ... . Continuing this rule, the number obtained from the 14th position is \\(14^2=196\\). It is not necessary to count every term individually. Taking the positive square root gives the term number because sequence positions are positive integers. The supplied answer A and its reasoning are accurate.

This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.