What is the next number in the series: 5, 7, 10, 12, 15, 17, 20, _?

To determine the next number in the series, it's essential to analyze the pattern in the given sequence: 5, 7, 10, 12, 15, 17, 20.

The series alternates between two different sets of increments. If we break down the transitions, we see the following:

• From 5 to 7, there is an increase of 2.

• From 7 to 10, the increase is 3.

• From 10 to 12, the increase is 2.

• From 12 to 15, the increase is 3.

• From 15 to 17, the increase is 2.

• From 17 to 20, the increase is 3.

In this sequence, it alternates between adding 2 and adding 3. Continuing this pattern, after reaching 20 (which is the last number in the series), the next operation would be to add 2. Therefore, the next number would be:

20 + 2 = 22.

This analysis confirms that 22 is the correct next number in this alternating sequence, following the established pattern of increments.