Find the number of terms in the progression `8+ 12+16+……+124`.

Explanation

To find the number of terms in the arithmetic progression (AP) given by the series \(8, 12, 16, \ldots, 124\), we can follow these steps:

### Step 1: Identify the first term and the common difference
The first term \(a\) of the AP is \(8\). The common difference \(d\) can be calculated as follows:
\[ d = 12 - 8 = 4 \]
Thus, the common difference \(d\) is \(4\).

### Step 2: Identify the last term
The last term of the AP is given as \(124\).

### Step 3: Use the formula for the nth term of an AP
The formula for the nth term \(a_n\) of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]
In this case, we need to find \(n\) such that \(a_n = 124\). Substituting the known values into the formula gives:
\[ 124 = 8 + (n - 1) \cdot 4 \]

### Step 4: Solve for \(n\)
First, we simplify the equation:
\[ 124 - 8 = (n - 1) \cdot 4 \]
\[ 116 = (n - 1) \cdot 4 \]
Now, divide both sides by \(4\):
\[ n - 1 = \frac{116}{4} \]
\[ n - 1 = 29 \]
Adding \(1\) to both sides gives:
\[ n = 29 + 1 = 30 \]

### Conclusion
The number of terms in the progression is \(30\).