Find the missing term in given sequence    36,72,24,96,?,1115.2

Let's analyze the sequence: 36, 72, 24, 96, ?, 1115.2.

The sequence alternates between two patterns: 
- The first pattern involves multiplying by a factor.
- The second pattern involves dividing by a factor.

### Step 1: Look at the pattern for the odd-position terms (1st, 3rd, and 5th).
- 36 → 24 → ?
It looks like the first number is decreasing.
- To find the factor between 36 and 24, let's divide 36 by 1.5:
  
  \[
  36 \div 1.5 = 24
  \]
- This suggests a factor of 1.5.

Thus, to find the next term (the 5th term), we divide 24 by 1.5:
\[
24 \div 1.5 = 16
\]

So, the missing term is **16**.

### Step 2: Verify the even-position terms (2nd, 4th, and 6th).
- 72 → 96 → 1115.2
It appears that these terms are increasing by a multiplication factor.
- To find the factor between 72 and 96, divide 96 by 72:
  
  \[
  96 \div 72 = 1.3333 \text{ (approximately)}
  \]
- Now, check the factor between 96 and 1115.2:
  
  \[
  1115.2 \div 96 = 11.64
  \]
Thus, the terms are multiplying by different factors at each step.

### Conclusion:
The missing term in the sequence is **16**.

Would you like to see more details or have any questions about this process?

### 5 Related Questions:
1. How do you identify alternating sequences in a given series?
2. What are some strategies to spot patterns involving multiplication and division?
3. How can you test if a sequence follows a geometric progression?
4. What other types of sequences commonly use alternating multiplication and division?
5. How can you use differences and ratios to analyze sequences?

### Tip:
When solving sequences, always check for alternating patterns or common differences and ratios between terms, as they often help in identifying the correct pattern.

Find the missing term in given sequence 36,72,24,96,?,1115.2

Learn how to solve the missing term in the alternating sequence 36,72,24,96,?,1115.2. This problem involves identifying a pattern of multiplication and division between alternating terms. Step-by-step solution for students in Grades 6-8.

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