7,8,18,57,228,1165,6996:

Options

A. 8
B. 18
C. 57
D. 228

Answer

To find the odd term in the series 7, 8, 18, 57, 228, 1165, 6996, we will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
We will look for a pattern in the series. The first term is 7. Let's see how each term relates to the next.

2. **Calculate the Next Terms**:
- From 7 to 8:
\[ 7 \times 1 + 1 = 8 \]
- From 8 to 18:
\[ 8 \times 2 + 2 = 18 \]
- From 18 to 57:
\[ 18 \times 3 + 3 = 54 + 3 = 57 \]
- From 57 to 228:
\[ 57 \times 4 + 4 = 228 + 4 = 228 \]
- From 228 to 1165:
\[ 228 \times 5 + 5 = 1140 + 5 = 1145 \quad (\text{This is where we suspect an error}) \]
- From 1165 to 6996:
\[ 1165 \times 6 + 6 = 6990 + 6 = 6996 \]

3. **Identify the Wrong Term**:
- We found that the calculation from 228 to 1165 does not hold true as it should yield 1145, not 1165. Therefore, the term that does not fit the pattern is **1165**.

4. **Conclusion**:
The odd term in the series is **1165**.