Series Question

Determine the number which will come in place of ‘?’ in the following series: Bank PO 2018

1.5, 4, 20, 126, ?, 10265

A) 1024  B) 1142  C) 1044  D) 1052  E) 1548

Answer: Question is wrong.

The series is inconsistent or mistake in the values of 1.5, 4, 20 or 126

To prove that this question is mathematically invalid, you can use the following technical breakdown. It demonstrates that the series lacks a common underlying formula and that the options provided do not satisfy any reasonable progression.

Arguments for Question Invalidation

Lack of a Uniform Pattern

In a logical series, the rule applied to each term must be consistent. Let's attempt to find a rule (n * multiplier + constant):

Step 1: (1.5 * 2) + 1 = 4

Step 2: (4 * 4) + 4 = 20

Step 3: (20 * 6) + 6 = 126

At this stage, the multipliers (2, 4, 6) are consistent. However, the constants added (1, 4, 6) follow no mathematical sequence. There is no logical reason for the addition to jump from 1 to 4 and then to 6.

Violation of the Final Term

If we assume the next multiplier is 8 (continuing the 2, 4, 6 trend) and the addition is also 8 (matching the previous two steps), the calculation would be:

(126 * 8) + 8 = 1016

Not only is 1016 missing from the options, but it also fails to lead to the final term of 10265. To reach 10265 from any of the given options using a multiplier of 10, the constant would have to be an arbitrary, non-patterned number:

If ? was 1048, the next step is (1048 * 10) - 215 = 10265.

If ? was 1024, the next step is (1024 * 10) + 25 = 10265.

The addition of -215 or 25 shows that the series creator "forced" the numbers rather than following a logic.

Option Discrepancy

The value often cited as the answer to this broken series in various forums is 1048. However, 1048 is not listed in your options (1024, 1142, 1044, 1052, 1548).

Option 1 (1024): (126 * 8) + 16. (Adding 16 doesn't fit the previous additions of 1, 4, 6).

Option 3 (1044): (126 * 8) + 36. (Adding 36 doesn't fit).

Option 4 (1052): (126 * 8) + 44. (Adding 44 doesn't fit).

Conclusion

A series is considered "wrong" or "invalid" if it requires a different, unrelated rule for every single step. Since this sequence requires the arbitrary selection of constants to match the next term, it fails the basic test of a logical progression. The absence of a mathematically derivable answer among the options further proves a typographical error in the question's design.