Which term of the AP 72, 63, 54, … is 0?

Options

A. 8th
B. 9th
C. 10th
D. 11th

Explanation

To find which term of the arithmetic progression (AP) 72, 63, 54, … is equal to 0, we can follow these steps:

### Step 1: Identify the first term (a) and the common difference (d)
The first term \( a \) of the AP is 72. To find the common difference \( d \), we subtract the first term from the second term:
\[ d = 63 - 72 = -9 \]

### 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 need to find \( n \) such that \( T_n = 0 \).

### Step 3: Set up the equation
Substituting the values of \( T_n \), \( a \), and \( d \) into the formula:
\[ 0 = 72 + (n - 1)(-9) \]

### Step 4: Simplify the equation
Rearranging the equation:
\[ 0 = 72 - 9(n - 1) \]
This simplifies to:
\[ 0 = 72 - 9n + 9 \]
Combining like terms gives:
\[ 0 = 81 - 9n \]

### Step 5: Solve for n
Now, we can solve for \( n \):
\[ 9n = 81 \]
\[ n = \frac{81}{9} = 9 \]

### Conclusion
Thus, the term of the AP that is equal to 0 is the 9th term.

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