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What should come is place of the qu...

What should come is place of the question mark (?) in the following number series ?
`5" " 54" "90" "115" "131" "140" "?`

A

149

B

144

C

142

D

152

Text Solution

AI Generated Solution

The correct Answer is:
To find the missing number in the series `5, 54, 90, 115, 131, 140, ?`, we will analyze the differences between consecutive terms. ### Step-by-Step Solution: 1. **List the numbers in the series:** \[ 5, 54, 90, 115, 131, 140, ? \] 2. **Calculate the differences between consecutive terms:** - Difference between 54 and 5: \[ 54 - 5 = 49 \] - Difference between 90 and 54: \[ 90 - 54 = 36 \] - Difference between 115 and 90: \[ 115 - 90 = 25 \] - Difference between 131 and 115: \[ 131 - 115 = 16 \] - Difference between 140 and 131: \[ 140 - 131 = 9 \] So, the differences are: \[ 49, 36, 25, 16, 9 \] 3. **Identify the pattern in the differences:** The differences are: \[ 7^2, 6^2, 5^2, 4^2, 3^2 \] This indicates that the next difference should be: \[ 2^2 = 4 \] 4. **Calculate the next term using the identified pattern:** - The last term we have is 140. To find the next term, we add the next difference (4): \[ 140 + 4 = 144 \] 5. **Conclusion:** The missing number in the series is: \[ \boxed{144} \]
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