In the series 7, 11, 19, 35, ?, find the next number by examining the pattern in the successive differences between terms.

Introduction / Context:
This is a classic number series question where we must determine the next term. The numbers 7, 11, 19 and 35 increase at an accelerating pace, which suggests that the differences between consecutive terms themselves follow a pattern. Spotting this pattern is the key to finding the missing value.

Given Data / Assumptions:
The series given is:

• 7
• 11
• 19
• 35
• ?

We assume that a consistent rule governs the difference between one term and the next, and that this rule can be extended to compute the unknown term.

Concept / Approach:
When numbers increase at a non constant rate, it is helpful to compute the first differences between consecutive terms. If these differences form a simple pattern such as doubling, increasing by a fixed amount or following a small arithmetic progression, we can use that pattern to obtain the next difference and hence the next term.

Step-by-Step Solution:
Step 1: Compute the first differences.From 7 to 11 the difference is 11 − 7 = 4.From 11 to 19 the difference is 19 − 11 = 8.From 19 to 35 the difference is 35 − 19 = 16.Step 2: Observe that the differences are 4, 8 and 16, which clearly double each time.Step 3: Following this pattern, the next difference should be 16 * 2 = 32.Step 4: Therefore, the next term in the series is 35 + 32 = 67.

Verification / Alternative check:
We can restate the series in terms of the rule: start from 7 and repeatedly add differences that double each step. So we have 7, then 7 + 4 = 11, then 11 + 8 = 19, then 19 + 16 = 35, and finally 35 + 32 = 67. This process gives a clean, consistent sequence with no contradictions, confirming that 67 is the unique logical continuation.

Why Other Options Are Wrong:
Values 131, 94 and 83 do not equal 35 + 32, so they do not respect the doubling difference pattern. If we used any of them, the differences between terms would no longer form the simple sequence 4, 8, 16, 32. Hence those values are not compatible with the observed rule governing the series.

Common Pitfalls:
Some students may attempt to find a direct multiplication rule from term to term, which does not work well here because the ratio varies. Focusing on first differences is a much more effective strategy whenever you see a steadily increasing but non constant gap between numbers in a series.

Final Answer:
The next number in the given series is 67.