Question

Look carefully for the pattern, and then choose which pair of numbers comes next: 4 7 26 10 13 20 16

• A. 14 4
• B. 14 17
• C. 18 14
• D. 19 13
• E. 19 14

Hint:

When a series fluctuates (goes up, then up, then down significantly), it is almost always an interleaved series. Try skipping 1 or 2 numbers to find the hidden arithmetic pattern.

Answer 1

Answer: (E)

Concept:
In complex number series, there are often multiple patterns running concurrently (interleaved series). To identify them, try looking at every second or third number to see if a consistent arithmetic progression exists.

Step 1: Identify the interleaved series.
Let's split the sequence into three alternating series:
• Series 1 (1st, 4th, 7th terms): 4, 10, 16...
Pattern: $+6$ ($4+6=10, 10+6=16$). The next term in this series would be $16+6 = 22$.
• Series 2 (2nd, 5th terms): 7, 13...
Pattern: $+6$ ($7+6=13$). The next term in this series (the 8th term) is $13+6 = \mathbf{19}$.
• Series 3 (3rd, 6th terms): 26, 20...
Pattern: $-6$ ($26-6=20$). The next term in this series (the 9th term) is $20-6 = \mathbf{14}$.

Step 2: Combine the results to find the next pair.
The sequence follows the order: (Series 1, Series 2, Series 3).
The last term given is 16 (Series 1). The next two terms must belong to Series 2 and Series 3 respectively.
• Next term: 19
• Following term: 14 The next pair is 19 14.