In the alternating difference series 2, 19, 0, 21, -2, ?, find the next term by identifying the pattern of adding and subtracting consecutive odd numbers.

Introduction / Context:
This series moves up and down: 2, 19, 0, 21, -2, ?. The jumps between terms are fairly large and alternate in sign, which hints that the series is constructed by adding and subtracting odd numbers in sequence. Recognising this type of alternating pattern is essential for many reasoning questions.

Given Data / Assumptions:
The known terms are:

• 2
• 19
• 0
• 21
• -2
• ?

We assume that each step involves adding or subtracting an odd integer that itself follows a simple sequence, likely consecutive odd numbers such as 17, 19, 21, 23, 25, and so on.

Concept / Approach:
The first step is to compute the differences between consecutive terms and see whether they match a pattern of odd numbers with alternating signs. Once we recognise the sequence of differences, we extend it to obtain the next term in the main series.

Step-by-Step Solution:
Step 1: Compute consecutive differences.From 2 to 19: 19 - 2 = +17.From 19 to 0: 0 - 19 = -19.From 0 to 21: 21 - 0 = +21.From 21 to -2: -2 - 21 = -23.Step 2: Observe the pattern in the differences: +17, -19, +21, -23.Step 3: These are consecutive odd numbers 17, 19, 21, 23 with alternating plus and minus signs.Step 4: The next difference should follow the same rule and be +25, the next odd number, with a positive sign.Step 5: Therefore, the next term is -2 + 25 = 23.

Verification / Alternative check:
We can summarise the pattern as: start at 2, then repeatedly add or subtract consecutive odd numbers starting from 17 with alternating signs. That is, 2 + 17 = 19, 19 - 19 = 0, 0 + 21 = 21, 21 - 23 = -2, and -2 + 25 = 23. This reconstruction reproduces all the given terms and supplies a single consistent next term.

Why Other Options Are Wrong:
Values 25, 27 and 29 would require differences of 27, 29 or 31 from -2, which would break the clean progression of odd differences 17, 19, 21, 23, 25. Only 23 gives a next difference of +25, so the other options do not match the identified pattern.

Common Pitfalls:
Some learners may look only at the absolute sizes of the numbers and not notice how the differences alternate between positive and negative. Others may try to fit a multiplication rule, which does not work with the presence of negative terms. Checking the differences and seeing whether they follow a nice sequence such as consecutive odd numbers is often the fastest path to the solution.

Final Answer:
The next number in the series, obtained by adding 25 to -2, is 23.