Which of the following numbers will replace the question mark in the given series 7 19 4 1 25 ........

General Intelligence and Reasoning (CHSL) Number series

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Which of the following numbers will replace the question mark (?) in the given series?

7, 19, 4, ?, 1, 25

This questions was previously asked in

SSC CHSL 8th June 2022 Shift-2

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Explanation:

Correct option 2: 22

Analyzing the Number Series Pattern
The question asks us to find the number that replaces the question mark (?) in the given series:
7, 19, 4, ?, 1, 25
To solve number series problems, we need to identify the underlying pattern or rule that connects the terms.
Identifying the Interleaved Series Pattern
Let's examine the numbers closely. Sometimes, the pattern might not involve consecutive terms but alternate terms or groups of terms. Looking at the given series:

7, 19, 4, ?, 1, 25

Let's separate the terms at odd positions (1st, 3rd, 5th, ... ) and the terms at even positions (2nd, 4th, 6th, ... ).
Sub-series 1: Terms at Odd Positions
The terms at odd positions are 7 (1st), 4 (3rd), and 1 (5th).
Let's look at the difference between consecutive terms in this sub-series:

Difference between 1st and 3rd term: 4−7=−3
Difference between 3rd and 5th term: 1−4=−3

There is a consistent difference of -3 between consecutive terms in this sub-series. This indicates an arithmetic progression with a common difference of -3.
Sub-series 2: Terms at Even Positions
The terms at even positions are 19 (2nd), ? (4th), and 25 (6th).
This sub-series contains the missing number. Let's assume this sub-series also follows a pattern, possibly an arithmetic progression.
If it's an arithmetic progression, the common difference would be constant. Let the missing term (4th position) be 'x'. The terms are 19, x, 25.
The difference between the 4th and 2nd term would be x−19
The difference between the 6th and 4th term would be 25−x
For an arithmetic progression, these differences must be equal:
x−19=25−x
Let's solve for x:
x+x=25+19
2x=44
?x=22
Let's check if the common difference is constant with x = 22:
Difference between 4th and 2nd term: 22−19=3
Difference between 6th and 4th term: 25−22=3
Yes, there is a consistent difference of +3 between consecutive terms in this sub-series. This indicates an arithmetic progression with a common difference of +3.
Determining the Missing Number
The missing number is in the 4th position, which belongs to the second sub-series (even positions). Based on our analysis of the second sub-series (19, ?, 25) following an arithmetic progression with a common difference of +3, the number replacing the question mark is 19+3=2219+3=22. The series for even positions is 19, 22, 25.

Summary of the Pattern