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5, 6, 10, 19, 35 ?...

5, 6, 10, 19, 35 ?

A

50

B

55

C

60

D

71

Text Solution

AI Generated Solution

The correct Answer is:
To find the missing number in the series: 5, 6, 10, 19, 35, we will analyze the differences between consecutive terms and identify a pattern. ### Step-by-Step Solution: 1. **Identify the series**: The given series is 5, 6, 10, 19, 35. 2. **Calculate the differences between consecutive terms**: - Difference between 6 and 5: \[ 6 - 5 = 1 \] - Difference between 10 and 6: \[ 10 - 6 = 4 \] - Difference between 19 and 10: \[ 19 - 10 = 9 \] - Difference between 35 and 19: \[ 35 - 19 = 16 \] 3. **List the differences**: The differences we calculated are 1, 4, 9, and 16. 4. **Recognize the pattern in the differences**: - The differences are: - 1 (which is \(1^2\)) - 4 (which is \(2^2\)) - 9 (which is \(3^2\)) - 16 (which is \(4^2\)) - This indicates that the differences are perfect squares of consecutive integers. 5. **Predict the next difference**: - Following the pattern, the next difference should be \(5^2 = 25\). 6. **Calculate the next term in the series**: - To find the next term after 35, we add the next difference (25) to 35: \[ 35 + 25 = 60 \] 7. **Conclusion**: The missing number in the series is 60. ### Final Answer: The missing number is **60**. ---
To find the missing number in the series: 5, 6, 10, 19, 35, we will analyze the differences between consecutive terms and identify a pattern. ### Step-by-Step Solution: 1. **Identify the series**: The given series is 5, 6, 10, 19, 35. 2. **Calculate the differences between consecutive terms**: - Difference between 6 and 5: ...
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