If 100 times the `100^(t h)` term of an AP with non zero common difference equals the 50 times its `50^(t h)` term, then the `150^(t h)` term of this AP is (1) ` 150` (2) 150 times its `50^(t h)` term (3) 150 (4) zero

Options

A. 150 times its 50th term
B. 150
C. zero
D. -150

Explanation

To solve the problem, we need to find the \(150^{th}\) term of an arithmetic progression (AP) given that \(100\) times the \(100^{th}\) term equals \(50\) times the \(50^{th}\) term.

Let's denote:
- \(a\) as the first term of the AP
- \(d\) as the common difference of the AP

The \(n^{th}\) term of an AP is given by the formula:
\[
...