Find the next number in the given number sequence: 9, 19, 21, 43, 45, ...

Introduction / Context:
This series question uses an alternating pattern of operations: one step multiplies and adds a constant, the next step simply adds a smaller constant. Such patterns are popular in reasoning tests because they appear irregular unless the candidate checks each consecutive pair carefully. We must find the next term after 9, 19, 21, 43, 45.

Given Data / Assumptions:
- Sequence: 9, 19, 21, 43, 45, ?- The series alternates between larger and smaller jumps.- The pattern is expected to use simple integer operations.

Concept / Approach:
We examine how each term is derived from the previous one. By computing both products and sums, we can detect whether there is a repeating two-step rule. In particular, we test whether there is a rule of multiplying by 2 and adding 1 in one step, and then adding 2 in the next step, which is a common kind of alternating pattern in exam series.

Step-by-Step Solution:
- From 9 to 19: 9 * 2 + 1 = 18 + 1 = 19.- From 19 to 21: 19 + 2 = 21.- From 21 to 43: 21 * 2 + 1 = 42 + 1 = 43.- From 43 to 45: 43 + 2 = 45.- We observe a stable repeating pattern: • Step 1: multiply by 2 and add 1. • Step 2: add 2.- To find the next term, we apply the next operation in the cycle, which is again multiply by 2 and add 1.- So the next term after 45 is: 45 * 2 + 1 = 90 + 1 = 91.

Verification / Alternative check:
- Rewriting the pattern: 9 → (9 * 2 + 1) = 19 → (19 + 2) = 21 → (21 * 2 + 1) = 43 → (43 + 2) = 45 → (45 * 2 + 1) = 91.- The two-step cycle is consistently preserved across all transitions, and 91 fits perfectly into this structure.

Why Other Options Are Wrong:
- 88, 54, 49 and 73 do not equal 45 * 2 + 1.- Substituting any of these values breaks the simple alternation between multiplying and adding fixed constants.

Common Pitfalls:
- Candidates may only look at differences (10, 2, 22, 2) without noticing that larger jumps are exactly double plus one of the previous term.- It is easy to overlook the alternating pattern and assume a more complex nonlinear relation that is not needed.- Guessing without verifying each step against a consistent rule can lead to plausible sounding but incorrect answers.

Final Answer:
The pattern alternates between multiplying by 2 and adding 1 and then adding 2, so the next term is 45 * 2 + 1 = 91.