Which term of the A.P. 27, 24, 21,…..is zero?

Options

A. 9th
B. 7th
C. 6th
D. 10th

Answer

To find which term of the arithmetic progression (A.P.) 27, 24, 21, ... is zero, we can follow these steps:

### Step 1: Identify the first term and common difference
The first term \( a \) of the A.P. is 27. The common difference \( d \) can be calculated as:
\[ d = 24 - 27 = -3 \]
Thus, \( a = 27 \) and \( d = -3 \).

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

### Step 3: Set up the equation
Substituting \( a \) and \( d \) into the formula, we set \( a_n = 0 \):
\[ 0 = 27 + (n - 1)(-3) \]

### Step 4: Solve for \( n \)
Rearranging the equation:
\[ 0 = 27 - 3(n - 1) \]
\[ 3(n - 1) = 27 \]
\[ n - 1 = \frac{27}{3} \]
\[ n - 1 = 9 \]
\[ n = 9 + 1 \]
\[ n = 10 \]

### Conclusion
The 10th term of the given A.P. is 0.