Find the missing term in given series.

pq__sp__rs__qrs

To find the missing terms in the series \( pq\_\_sp\_\_rs\_\_qrs \), let's analyze the pattern.

### Given series:
\[ pq\_\_sp\_\_rs\_\_qrs \]

### Step 1: Identify the known terms and their order
- The series includes sequences such as \( pq \), \( sp \), \( rs \), and \( qrs \).
- The missing terms might complete or extend these sequences.

### Step 2: Look for a pattern in the sequence formation
- We see that the sequence \( pq \) is followed by \( sp \), which is followed by \( rs \), and ends with \( qrs \).

### Step 3: Analyze and fill in the blanks
- The pattern seems to involve cyclic permutations of the letters \( p, q, r, s \).
- After \( pq \), we should have a sequence starting with \( r \), as \( p \) and \( q \) have been used.
- Following \( sp \), we need to use the letter \( q \), which hasn't been used yet after \( sp \).
- After \( rs \), the sequence would likely involve \( p \), as it's the only letter missing in the context.

### Step 4: Complete the sequence
Given the analysis:
- The missing term after \( pq \) should be \( r \).
- The missing term after \( sp \) should be \( q \).
- The missing term after \( rs \) should be \( p \).

So, the complete sequence should be:
\[ pqr, spq, rsp, qrs \]

### Final Answer:
The missing terms in the series are **r, q, p**.

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Would you like a more detailed explanation, or do you have any further questions?

Here are some related questions for practice:

1. What is the next term in the series \( pqr, spq, rsp, qrs, \_\_ \)?
2. Can you identify the pattern if the series was \( pq, sp, rs, \_\_, qrs \)?
3. How do you determine the next term in a cyclic permutation series?
4. What happens if the sequence \( pqrs \) is repeated continuously?
5. How can permutation patterns be used in combinatorial problems?
6. What if the series started with \( sp \) instead of \( pq \)? What would the missing terms be?
7. Can you create a similar series with different letters or symbols?
8. How does understanding permutations help in solving complex series?

**Tip:** When analyzing series, especially those involving permutations, consider all elements and check for cyclic patterns.

Discover how to find the missing terms in the series pq__sp__rs__qrs through pattern recognition and analysis. This problem involves identifying cyclic permutations and completing sequences based on given patterns.

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