Three numbers are in GP whose sum is 70. If the extremes be each multiplied by 4 and the mean by 5, then they will be in AP. Find the numbers.

Explanation

To solve the problem step by step, we will denote the three numbers in geometric progression (GP) as follows:

Let the three numbers be:
- First term: \( a \)
- Second term: \( ar \)
- Third term: \( ar^2 \)

### Step 1: Set up the equation for the sum of the numbers
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