In the series 18, 97, 26, 91, ?, 83, find the missing number that correctly completes the pattern.

Introduction / Context:
This question involves a number series where two interleaved sequences are hidden inside one combined list. Many exam level series questions use this technique, alternating between two simpler patterns placed in a single sequence. Being able to separate and analyze these subsequences is an important skill in quantitative aptitude.

Given Data / Assumptions:

• The complete series is: 18, 97, 26, 91, ?, 83.
• We assume a single missing number that will make the pattern consistent.
• The series likely consists of two separate patterns, one in the odd positions and one in the even positions.

Concept / Approach:
We examine the numbers in odd positions and even positions separately. Often one subsequence is increasing in a simple way while the other decreases or changes with another rule. Here, 18, 26 and the missing term appear in the odd positions, while 97, 91 and 83 appear in the even positions. We will look at each subsequence independently.

Step-by-Step Solution:
Write odd positioned terms: 1st, 3rd and 5th terms are 18, 26 and ?.Write even positioned terms: 2nd, 4th and 6th terms are 97, 91 and 83.Consider the odd subsequence: 18, 26, ?. The difference between 26 and 18 is 8. A natural and simple pattern is to add 8 each time.So the next odd term would be 26 + 8 = 34.Consider the even subsequence: 97, 91, 83. Here the differences are 97 - 91 = 6 and 91 - 83 = 8. The decreases are 6 and then 8, which are increasing even numbers.This indicates that one subsequence increases by 8 while the other decreases by increasing even numbers, which is a reasonable and consistent structure.

Verification / Alternative check:
If we reconstruct the full series with the found value, we get: 18, 97, 26, 91, 34, 83. The odd subsequence 18, 26, 34 clearly grows by 8 each time. The even subsequence 97, 91, 83 decreases by 6 and then 8, forming a simple pattern of decreasing even differences. No other candidate among the options satisfies both subsequences as neatly.

Why Other Options Are Wrong:
32, 30 and 28 do not maintain the odd subsequence as an arithmetic progression with difference 8.

36 makes the odd subsequence 18, 26, 36 which has differences 8 and 10 and breaks the simplest pattern. None of these alternatives gives such a clean structure in both subsequences as 34 does.

Common Pitfalls:
Some students try to connect consecutive numbers in the total series directly, which looks irregular and confusing. The key is to notice possible interleaving patterns. Once you separate positions into odd and even, the arithmetic progression for one subsequence and the controlled decrease in the other become much easier to see.

Final Answer:
The missing term in the series is 34.