Soppose that all the terms of an arithmetic progression (AP) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is `6:11` and the seventh term lies between 130 and 140, then the common difference of this AP is

Explanation

To solve the problem, we need to find the common difference \( d \) of an arithmetic progression (AP) given the ratio of the sums of the first seven and eleven terms, and the condition on the seventh term.

### Step-by-Step Solution:

1. **Understanding the Sum of Terms in AP**:
The sum of the first \( n \) terms of an AP can be calculated using the formula:
\[
S_n = \frac{n}{2} \times (2a + (n-1)d)
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