If in a reaction `A rarr` Products, the concentrations of reactant `A` are `c_(0), ac_(0), a^(2)c_(0) a^(3)c_(0)`, …after time interval `0,t,2t,3t`…. Where `a` is constant, given, `0 lt alt 1`, show that the reaction is of first order. Also calculate the relation in `k, a`, and `t`.

Explanation

To solve the problem, we need to show that the reaction is of first order and derive the relationship between the rate constant \( k \), the constant \( a \), and the time \( t \).

### Step-by-Step Solution:

1. **Understanding the Concentrations**:
- At time \( t = 0 \), the concentration of \( A \) is \( c_0 \).
- At time \( t = T \), the concentration is \( ac_0 \).
- At time \( t = 2T \), the concentration is \( a^2c_0 \).
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