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 150th term of an arithmetic progression (AP) given that 100 times the 100th term equals 50 times the 50th term. Let's break this down step by step.

### Step 1: Define the terms of the AP
The general term of an arithmetic progression can be expressed as:
\[ T_n = a + (n-1)d \]
where \( a \) is the first term and \( d \) is the common difference.
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