Question: User: if i see this arithmetic sequences "144, 145, Q, 147, 148, 149, 150, 151, 152", i think that "Q = 146", since 146 appear between 145 and 147, with another word 146 comes after 145, that makes Q value is 146

1. **State the problem:** We are given an arithmetic sequence: $$144, 145, Q, 147, 148, 149, 150, 151, 152$$ and need to find the value of $$Q$$. 2. **Recall the definition of an arithmetic sequence:** In an arithmetic sequence, the difference between consecutive terms is constant. This difference is called the common difference $$d$$. 3. **Find the common difference:** From the given terms, observe that $$145 - 144 = 1$$ and $$147 - 145 = 2$$ if we assume $$Q$$ is unknown. But since the sequence is arithmetic, the difference must be the same between all consecutive terms. 4. **Use the known terms to find $$d$$:** Since $$144, 145$$ are consecutive, $$d = 145 - 144 = 1$$. 5. **Find $$Q$$ using the common difference:** Since $$Q$$ comes after $$145$$, $$Q = 145 + d = 145 + 1 = 146$$. 6. **Verify the next term:** The term after $$Q$$ is $$147$$, and $$147 - 146 = 1$$, which matches the common difference. 7. **Conclusion:** The value of $$Q$$ is $$146$$. This confirms your reasoning that $$Q = 146$$ because it fits the arithmetic sequence with common difference $$1$$.