If the arithmetic progression whose common difference is nonzero the sum of first `3n` terms is equal to the sum of next `n` terms. Then, find the ratio of the sum of the `2n` terms to the sum of next `2n` terms.

Options

A. `(1)/(5)`
B. `(2)/(3)`
C. `(3)/(4)`
D. None of these

Explanation

To solve the problem, we will follow these steps:

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

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