In the following series, one term is missing. Using the observed pattern of sums, find the number that should replace the question mark: 19, 26, 45, 71, 116, ?

Introduction / Context:
This series problem involves a pattern where each term after the first two appears to be related to the sum of earlier terms. Such Fibonacci style or additive sequences are frequently used in reasoning exams and require you to look beyond simple differences or ratios.

Given Data / Assumptions:
The series is:
19, 26, 45, 71, 116, ?
We assume that after the first two terms, each new term may be generated using a rule involving the previous terms, typically the sum of the last two numbers.

Concept / Approach:
A natural approach is to check whether each term from the third onward is equal to the sum of the two immediately preceding terms. If this holds for multiple consecutive terms, it is very likely that the pattern is additive. This idea is similar to the famous Fibonacci sequence, although here the starting values are different.

Step-by-Step Solution:
Step 1: Check the third term.19 + 26 = 45, which matches the third term.Step 2: Check the fourth term.26 + 45 = 71, which matches the fourth term.Step 3: Check the fifth term.45 + 71 = 116, which matches the fifth term.Step 4: Since the pattern holds consistently, we now compute the next term as the sum of the last two known terms.71 + 116 = 187.Thus, the missing term is 187.

Verification / Alternative check:
We can reconstruct the entire series from the first two terms under the assumption that each next term equals the sum of its predecessors. Starting from 19 and 26, we generate 45, 71, 116, and then 187. This perfectly matches the given terms and extends the pattern without any contradictions, so the rule is fully consistent across the series.

Why Other Options Are Wrong:
Numbers such as 166, 172, 184, or 160 do not equal 71 + 116. Using any of them would remove the clear additive relationship that exists between consecutive terms. For example, if we tried 184, the sum of 71 and 116 would no longer give the next term, which breaks the underlying structure of the sequence.

Common Pitfalls:
Some students focus on differences between consecutive terms, which vary and do not show a simple pattern here. Others may suspect multiplication or division where an additive rule is more appropriate. When differences do not produce a regular progression, always consider whether each term could be the sum of the previous two terms.

Final Answer:
The number that correctly completes the series is 187.