Calculate the sum of square from 1 to 9.
A. 284
B. 285
C. 385
D. 380

Options

A. B
B. C
C. D
D. A

Answer

To calculate the sum of squares from 1 to 9, we can use the formula for the sum of squares of the first n natural numbers:

\[ \text{Sum of squares} = \frac{n(n + 1)(2n + 1)}{6} \]

### Step-by-Step Solution:

1. **Identify n**: In this case, we want the sum of squares from 1 to 9, so \( n = 9 \).

2. **Substitute n into the formula**:
\[ \text{Sum of squares} = \frac{9(9 + 1)(2 \times 9 + 1)}{6} \]

3. **Calculate \( n + 1 \) and \( 2n + 1 \)**:
- \( n + 1 = 9 + 1 = 10 \)
- \( 2n + 1 = 2 \times 9 + 1 = 18 + 1 = 19 \)

4. **Substitute these values back into the formula**:
\[ \text{Sum of squares} = \frac{9 \times 10 \times 19}{6} \]

5. **Calculate the product in the numerator**:
- First, multiply \( 9 \times 10 = 90 \)
- Then multiply \( 90 \times 19 = 1710 \)

6. **Divide by 6**:
\[ \frac{1710}{6} = 285 \]

### Final Answer:
The sum of squares from 1 to 9 is \( 285 \).

### Options:
- A. 284
- B. 285
- C. 385
- D. 380

The correct answer is **B. 285**.