Three numbers a, b, c, non-zero, form an arithmetic progression. Increasing a by 1 or increasing c by 2 results in a geometric progression. Then b equals :

Options

A. 16
B. 14
C. 12
D. 10

Answer

To solve the problem, we need to follow these steps:

### Step 1: Understanding the Arithmetic Progression (AP)
Given three numbers \(a\), \(b\), and \(c\) form an arithmetic progression, we know that:
\[ 2b = a + c \quad \text{(1)} \]