What should be the next term in the following series ?
12,24 , 72,144 ?

Answer

To find the next term in the series 12, 24, 72, 144, we can analyze the pattern in the series step by step.

### Step 1: Identify the pattern in the series
Let's write down the terms:
- 1st term: 12
- 2nd term: 24
- 3rd term: 72
- 4th term: 144

### Step 2: Find the relationship between consecutive terms
Now, let's look at how each term relates to the previous one:
- From 12 to 24: \( 12 \times 2 = 24 \)
- From 24 to 72: \( 24 \times 3 = 72 \)
- From 72 to 144: \( 72 \times 2 = 144 \)

### Step 3: Recognize the alternating multiplication pattern
We can see that the multiplication alternates between multiplying by 2 and multiplying by 3:
- 12 multiplied by 2 gives 24.
- 24 multiplied by 3 gives 72.
- 72 multiplied by 2 gives 144.

### Step 4: Predict the next operation
Following the established pattern, the next operation should be multiplying by 3 again since the pattern is 2, 3, 2, 3.

### Step 5: Calculate the next term
Now, we will multiply the last term (144) by 3:
\[ 144 \times 3 = 432 \]

### Conclusion
Thus, the next term in the series is **432**.

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