Question

Find out the wrong number in the FOLLOWING series. 30, -5, -45, -90, -145, -195, -255

• A. -145
• B. -255
• C. -195
• D. -5

Hint:

When the first-order differences are not constant, check the second-order differences. Here, the first-order differences form their own arithmetic progression. Find the term that breaks this progression to identify the error in the original series.

Answer 1

The Correct Option is A

Let's find the pattern by looking at the differences between consecutive terms. \[\begin{array}{rl} \bullet & \text{-5 - 30 = -35} \\ \bullet & \text{-45 - (-5) = -40} \\ \bullet & \text{-90 - (-45) = -45} \\ \bullet & \text{-145 - (-90) = -55} \\ \bullet & \text{-195 - (-145) = -50} \\ \bullet & \text{-255 - (-195) = -60} \\ \end{array}\] The sequence of differences is: -35, -40, -45, -55, -50, -60. There is a clear arithmetic progression in the differences: -35, -40, -45... The next difference should be -50.
Let's see where the pattern breaks.
-90 + (-50) = -140. The series has -145. This seems to be the error. Let's check if the rest of the series follows from -140.
The next difference should be -55.
-140 + (-55) = -195. (Matches) The next difference should be -60.
-195 + (-60) = -255. (Matches) The pattern holds if the term -145 is replaced by -140. Therefore, -145 is the wrong number.