Question

Which of the following could be the $n^{th}$ term of any AP?

• A. 3n + 5
• B. 3n² – 4n - 4
• C. n² + n + 1
• D. 1/n

Answer 1

The correct option is A

3n + 5

The generic form of the nth term of an AP = a + (n-1)d = a + nd – d = (a-d) + nd = k + nd, where k = a-d

$t_n$ = dn + k.

Observe that this is a linear equation in n (A first degree equation). So any sequence with the nth term as a linear equation in ‘n’ can only be an AP sequence.

If the expression for the nth term is a second degree or any other degree, we cannot ensure that the difference between successive terms is a constant, which is the essence of being an AP.