Question

Find the next number in the series 5, 20, 24, 6, 2, 8,

Answer 1

Correct Answer: 12

Write Down the Series

The given series is: 5, 20, 24, 6, 2, 8.

We need to find the next number after 8. To do that, we’ll look for a pattern in how the numbers change from one to the next.

Analyze the Changes Between Numbers

Let’s look at each pair of numbers and figure out what operation (like addition, subtraction, multiplication, or division) connects them.

• From 5 to 20:
  5 × 4 = 20
  So, the first operation is multiply by 4.
• From 20 to 24:
  20 + 4 = 24
  So, the second operation is add 4.
• From 24 to 6:
  24 ÷ 4 = 6
  So, the third operation is divide by 4.
• From 6 to 2:
  6 - 4 = 2
  So, the fourth operation is subtract 4.
• From 2 to 8:
  2 × 4 = 8
  So, the fifth operation is multiply by 4.

Identify the Pattern

Now, let’s list the operations we found:

• 5 to 20: ×4
• 20 to 24: +4
• 24 to 6: ÷4
• 6 to 2: -4
• 2 to 8: ×4

The operations are: ×4, +4, ÷4, -4, ×4.

Notice that the fifth operation (×4) is the same as the first operation (×4). This suggests the pattern repeats every 5 steps. So, the sequence of operations is:

×4, +4, ÷4, -4, ×4, and then it starts over with +4 (the second operation in the cycle).

Apply the Pattern to Find the Next Number

The last number in the series is 8, and the last operation was ×4 (from 2 to 8).

Since the pattern repeats, the next operation after ×4 is +4.

Apply this to the last number, 8:

8 + 4 = 12

So, the next number in the series is 12.

Double-Check the Pattern

Let’s confirm by looking at the series again: 5, 20, 24, 6, 2, 8, 12.

• 5 → 20: ×4
• 20 → 24: +4
• 24 → 6: ÷4
• 6 → 2: -4
• 2 → 8: ×4
• 8 → 12: +4

The operations follow the pattern we identified, which confirms our solution is correct.

Final Answer

The next number in the series is 12.