The sum of three numbers which are consecutive terms of an A.P. is `21`. If the second number is reduced by `1` and the third is increased by `1` we obtain three consecutive terms of a G.P. Find the numbers.

Explanation

To solve the problem step by step, we will first define the three consecutive terms of the arithmetic progression (A.P.) and then use the conditions given in the problem to find the values of these terms.

### Step 1: Define the terms of the A.P.
Let the three consecutive terms of the A.P. be:
- First term: \( A - D \)
- Second term: \( A \)
- Third term: \( A + D \)

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