Which term of the A.P. 90+87+84+…is zero ?

Explanation

To find which term of the arithmetic progression (A.P.) 90, 87, 84, ... is zero, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (a) and the common difference (d):**
- The first term \( a = 90 \).
- The common difference \( d \) can be calculated as:
\[ d = 87 - 90 = -3 \]

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

3. **Set up the equation:**
- Substitute \( a = 90 \), \( d = -3 \), and \( a_n = 0 \) into the formula:
\[ 0 = 90 + (n - 1)(-3) \]

4. **Solve for n:**
- Rearranging the equation:
\[ 0 = 90 - 3(n - 1) \]
\[ 0 = 90 - 3n + 3 \]
\[ 0 = 93 - 3n \]
\[ 3n = 93 \]
\[ n = \frac{93}{3} = 31 \]

5. **Conclusion:**
- Therefore, the term of the A.P. that is zero is the **31st term**.