Which term of the series 72 63 54………is zero

Options

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

Answer

To find which term of the series 72, 63, 54, ... is zero, we can follow these steps:

### Step 1: Identify the series
The series given is 72, 63, 54, ...

### Step 2: Determine the common difference
To find the common difference (D), we can subtract consecutive terms:
- 63 - 72 = -9
- 54 - 63 = -9

Thus, the common difference \( D = -9 \).

### Step 3: Write the formula for the nth term of an arithmetic series
The nth term of an arithmetic series can be expressed as:
\[ A_n = A + (n - 1) \cdot D \]
where:
- \( A \) is the first term (72),
- \( D \) is the common difference (-9),
- \( n \) is the term number.

### Step 4: Set the nth term equal to zero
We want to find \( n \) such that:
\[ A_n = 0 \]
Substituting the values we have:
\[ 0 = 72 + (n - 1)(-9) \]

### Step 5: Solve for n
Rearranging the equation:
\[ 0 = 72 - 9(n - 1) \]
\[ 9(n - 1) = 72 \]
\[ n - 1 = \frac{72}{9} \]
\[ n - 1 = 8 \]
\[ n = 8 + 1 \]
\[ n = 9 \]

### Conclusion
The 9th term of the series is zero.

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