Find the next term in this series
`45,54, 64, 75` __________.

Options

A. 87
B. 89
C. 91
D. 90

Answer

To find the next term in the series `45, 54, 64, 75`, we will analyze the differences between the consecutive terms:

1. **Identify the terms**:
- The given series is: 45, 54, 64, 75.

2. **Calculate the differences between consecutive terms**:
- Difference between 54 and 45:
\[ 54 - 45 = 9 \]
- Difference between 64 and 54:
\[ 64 - 54 = 10 \]
- Difference between 75 and 64:
\[ 75 - 64 = 11 \]

3. **Observe the pattern in the differences**:
- The differences we calculated are: 9, 10, 11.
- We can see that the differences are increasing by 1 each time.

4. **Predict the next difference**:
- Following the pattern, the next difference should be:
\[ 11 + 1 = 12 \]

5. **Calculate the next term**:
- Now, we add this next difference to the last term in the series:
\[ 75 + 12 = 87 \]

6. **Conclusion**:
- Therefore, the next term in the series is **87**.