Consider the following numerical series: 4, 7, 12, 19, 28, \dots. What is the next number … — State PSC Exam

Consider the following numerical series: $4, 7, 12, 19, 28, \dots$ . What is the next number in this series?

Answer: 39

The next number in the series is

39

The difference between consecutive terms increases by 2 each time (

+3, +5, +7, +9

). The next difference to add is

+11

, yielding

28 + 11 = 39

Calculate the difference between each pair of consecutive terms.

The differences are

3, 5, 7, 9

Identifying the first-order difference sequence reveals the pattern of progression.

Find the next value in the difference sequence.

The next odd number after

9

11

The pattern of differences consists of consecutive prime/odd increments (specifically, odd numbers

+2

each step).

Add the calculated difference to the final given term of the series.

28 + 11 = 39

Applying the pattern to find the subsequent term.

Number series completion using a sequence of increasing odd differences.

Question