Consider the following numerical sequence: 11, 14, 23, 44, 83, \dots What is the next term… — State PSC Exam

Consider the following numerical sequence: $11, 14, 23, 44, 83, \dots$ What is the next term in this sequence?

Answer: 146

The next term in the sequence is 146.

The sequence follows a double-difference pattern where the differences between consecutive terms (

3, 9, 21, 39

) themselves differ by an arithmetic progression of multiples of 6 (

6, 12, 18

). Adding the next increment of 24 to 39 gives a term difference of 63. Adding 63 to the last term 83 results in 146.

Find the first difference between consecutive terms

The differences are 3, 9, 21, and 39.

Analyzing differences helps reveal underlying polynomial or double-difference patterns.

Find the second difference (difference of differences)

The second differences are 6, 12, and 18.

The first differences do not form an obvious basic sequence, so taking second differences reveals the hidden pattern.

Determine the next first-difference value

Next second difference is 24, making the next first difference 39 + 24 = 63.

The second-level differences increase by 6 each step (multiples of 6).

Calculate the next term in the sequence

83 + 63 = 146

Adding the computed term difference to the latest term yields the next sequence number.

Double Difference Number Series

Estimated Time:1m 30s

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