In the following decreasing number series, select the missing number that will correctly complete the pattern: 46, 41, 35, 30, ?, 19, 13.

Introduction / Context:
This question features a decreasing number series where the gaps between the terms are not constant but follow a repeating pattern. Such problems test your ability to observe alternating differences and to extend that alternation correctly to find the missing term in the middle of the sequence.

Given Data / Assumptions:
Given series: 46, 41, 35, 30, ?, 19, 13.One term is missing between 30 and 19.We assume that a simple repeating pattern in the differences governs the sequence.

Concept / Approach:
When a series decreases in an irregular way, it is often useful to compute consecutive differences and then look for repetition or alternation. Here, we expect that the decreases alternate between two fixed values. Once that alternation is confirmed, we use it to interpolate the missing term between known neighbours. This approach is standard in competitive exam number series questions.

Step-by-Step Solution:
Step 1: Compute 46 - 41 = 5.Step 2: Compute 41 - 35 = 6.Step 3: Compute 35 - 30 = 5.Step 4: The pattern so far is a decrease of 5, then 6, then 5 again, suggesting an alternating sequence of -5, -6, -5, -6, and so on.Step 5: Let the missing term be x. From 30 to x we must continue the pattern and subtract 6: x = 30 - 6 = 24.Step 6: Check the next step: 24 to 19 should subtract 5, and indeed 24 - 19 = 5, which matches the established alternation.

Verification / Alternative check:
Write the full series including the candidate term: 46, 41, 35, 30, 24, 19, 13. Now compute all differences: 46 - 41 = 5, 41 - 35 = 6, 35 - 30 = 5, 30 - 24 = 6, 24 - 19 = 5, and 19 - 13 = 6. The pattern is clearly an alternating sequence of -5, -6, -5, -6, -5, -6, validating 24 as the correct missing number.

Why Other Options Are Wrong:
Option 26 would give 30 - 26 = 4 and 26 - 19 = 7, which breaks the alternating differences of 5 and 6.Option 28 produces 30 - 28 = 2 and 28 - 19 = 9, completely inconsistent with the established pattern.Option 22 leads to 30 - 22 = 8 and 22 - 19 = 3, again failing to match any simple alternating difference rule.

Common Pitfalls:
Students sometimes try to average the surrounding terms instead of analyzing the full pattern of differences, which rarely works in non-linear series. Another mistake is to assume that all differences must be equal. Many exam questions deliberately use alternating or gradually changing differences to test deeper observation skills, so it is important to check multiple gaps before deciding on a pattern.

Final Answer:
The missing number that fits the alternating decrease pattern is 24.