Which term of the AP 72, 68, 64, 60, ..is 0?

Answer

To find which term of the arithmetic progression (AP) 72, 68, 64, 60, ... is equal to 0, we can follow these steps:

### Step 1: Identify the first term and common difference
The first term \( a \) of the AP is 72. The common difference \( d \) can be calculated as follows:
\[ d = 68 - 72 = -4 \]

### Step 2: Use the formula for the nth term of an AP
The formula for the nth term \( T_n \) of an arithmetic progression is given by:
\[ T_n = a + (n - 1) \cdot d \]
We want to find \( n \) such that \( T_n = 0 \).

### Step 3: Set up the equation
Substituting the known values into the formula:
\[ 0 = 72 + (n - 1)(-4) \]

### Step 4: Simplify the equation
Rearranging the equation gives:
\[ 0 = 72 - 4(n - 1) \]
\[ 0 = 72 - 4n + 4 \]
\[ 0 = 76 - 4n \]

### Step 5: Solve for \( n \)
Now, we can isolate \( n \):
\[ 4n = 76 \]
\[ n = \frac{76}{4} = 19 \]

### Conclusion
Thus, the 19th term of the given arithmetic progression is 0.