A series is given with one number missing. Choose the correct alternative from the given options that will complete the series: 2, 5, 10, 17, ?, 37

Introduction / Context:
This series grows by adding consecutive odd numbers. Number series of this form are very common in aptitude tests because they are simple yet require close attention to small differences. The given series is 2, 5, 10, 17, ?, 37 and we must find the missing term that fits the pattern of odd increments.

Given Data / Assumptions:
- Series: 2, 5, 10, 17, ?, 37.- The second last term is missing.- All terms are positive integers.- Differences appear to increase slowly, hinting at consecutive odd numbers such as 3, 5, 7, 9, 11.

Concept / Approach:
The method is to calculate consecutive differences between terms. If those differences are odd and increase by 2 each time, then we can extend this sequence of differences and use it to fill the missing value. This is a standard pattern of additive growth using odd numbers.

Step-by-Step Solution:
- From 2 to 5: 5 - 2 = 3.- From 5 to 10: 10 - 5 = 5.- From 10 to 17: 17 - 10 = 7.- The differences so far are 3, 5, 7, which are consecutive odd numbers increasing by 2.- The next differences in this sequence should be 9 and then 11.- Therefore, the next term after 17 is 17 + 9 = 26.- The final term should then be 26 + 11 = 37, which matches the given last term.

Verification / Alternative check:
- With 26 inserted, the full sequence is 2, 5, 10, 17, 26, 37.- The complete list of differences is 3, 5, 7, 9, 11, confirming the consecutive odd number pattern.- No other candidate produces this smooth progression of differences.

Why Other Options Are Wrong:
- 24, 30, 32 and 28 yield differences that do not match the required series 3, 5, 7, 9, 11.- For instance, 24 would give a difference of 7 from 17 and 13 from 24 to 37, breaking the consecutive odd step of 9 and 11.

Common Pitfalls:
- Some candidates may miscalculate one of the differences, making the pattern appear irregular.- Failing to recognise the standard sequence of odd numbers can lead to overcomplicated attempts using squares or cubes.- Guessing based on proximity to 37 without checking the full pattern can result in wrong choices like 30 or 32.

Final Answer:
The differences form the odd number sequence 3, 5, 7, 9, 11, so the missing term is 26.