In this number series aptitude question, find the next number in the series: 35, 36, 55, 111, ?

Introduction / Context:
This question examines your ability to detect a pattern where each term is generated by multiplying the previous term by an increasing factor and then adding a constant. The series 35, 36, 55, 111, ? is a good example of a slightly non-standard progression commonly used in aptitude tests.

Given Data / Assumptions:

• Series: 35, 36, 55, 111, ?
• We must determine the single correct next term.
• The pattern is consistent and uses the previous term to generate the next term.

Concept / Approach:
When differences between terms are not constant, it is often helpful to consider multiplicative patterns. Sometimes, the multiplier increases by a fixed amount, or alternates in a clear way. Here, we will examine both multiplication and addition together to reveal the rule that generates the next term.

Step-by-Step Solution:
Step 1: Check how 36 is related to 35.35 * 1 + 1 = 36.Step 2: Check how 55 is related to 36.36 * 1.5 + 1 = 54 + 1 = 55.Step 3: Check how 111 is related to 55.55 * 2 + 1 = 110 + 1 = 111.Step 4: Recognize the pattern in the multipliers.The factor is increasing by 0.5 each time: 1, 1.5, 2, and next will be 2.5, while we always add 1 at the end.Step 5: Apply the pattern to find the next term.Next term = 111 * 2.5 + 1 = 277.5 + 1 = 278.5.

Verification / Alternative check:
Rebuilding the series using the rule confirms consistency. Start from 35 and repeatedly apply multiply by 1, 1.5, 2, 2.5 and add 1 each time to obtain 36, 55, 111 and 278.5 respectively. The smooth increase in the multiplier by 0.5 and constant addition of 1 indicates this is the intended logic for the series.

Why Other Options Are Wrong:
264.5: This does not correspond to multiplying 111 by any natural step in the factor sequence 1, 1.5, 2, 2.5 plus 1.
212.5: This value would require a lower multiplier than 2.5, breaking the increasing multiplier pattern.
202: This is too small and cannot be generated by any reasonable continuation of the factor sequence used for earlier terms.

Common Pitfalls:
A frequent mistake is to consider only additive differences between terms and miss a hidden multiplication pattern. Another issue is to approximate the next term based on rough size instead of deriving it from a precise rule. Always inspect both differences and ratios, especially when the numbers grow faster than in a simple arithmetic progression.

Final Answer:
The next number in the series is 278.5.