The first three numbers in a series are -3 0 3 the 10th number in the series will be

Options

A. 18
B. 21
C. 24
D. 27

Answer

To find the 10th number in the series where the first three numbers are -3, 0, and 3, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the First Term (a)**:
The first term of the series is given as -3.
\[ a = -3 \]

2. **Determine the Common Difference (d)**:
To find the common difference, we subtract the first term from the second term:
\[ d = 0 - (-3) = 0 + 3 = 3 \]
We can also check this by subtracting the second term from the third term:
\[ d = 3 - 0 = 3 \]
Thus, the common difference \( d = 3 \).

3. **Use the nth Term Formula**:
The formula for the nth term of an arithmetic progression (AP) is given by:
\[ a_n = a + (n - 1) \cdot d \]
We need to find the 10th term, so we set \( n = 10 \):
\[ a_{10} = -3 + (10 - 1) \cdot 3 \]

4. **Calculate the 10th Term**:
Substitute \( n = 10 \) into the formula:
\[ a_{10} = -3 + 9 \cdot 3 \]
Calculate \( 9 \cdot 3 \):
\[ 9 \cdot 3 = 27 \]
Now, substitute back:
\[ a_{10} = -3 + 27 \]
Finally, calculate:
\[ a_{10} = 24 \]

5. **Conclusion**:
The 10th number in the series is \( 24 \).

### Final Answer:
The 10th number in the series is **24**.