Question

In the given number series: 12, 24, 21, 42, 39, 78 ...
Which number would come next?

Hint:

In alternating number series, identify the pattern (addition, subtraction, multiplication) and apply it consistently to predict the next term.

Answer 1

Step 1: Identifying the Pattern.
The given series alternates between multiplying by 2 and subtracting 3. Let's analyze the series: - \( 12 \to 24 \): Multiply by 2. - \( 24 \to 21 \): Subtract 3. - \( 21 \to 42 \): Multiply by 2. - \( 42 \to 39 \): Subtract 3. - \( 39 \to 78 \): Multiply by 2.
Step 2: Predicting the Next Step.
Following the alternating pattern, the next operation should be subtracting 3: \[ 78 - 3 = 75 \]
Step 3: Conclusion.
Thus, the next number in the series is \( 75 \).

\[ \boxed{75} \]