Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15

Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15
Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15

The Correct Answer and Explanation is:

Sequence Given:

2, 6, 3, 9, 6, 18, 15

Next Three Numbers:

45, 36, 108

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Explanation

To identify the next numbers in a sequence, we look for patterns—either arithmetic, geometric, alternating, or a combination. Let’s examine the given sequence:

2, 6, 3, 9, 6, 18, 15

Split the sequence into two interleaved patterns:

• Odd positions (1st, 3rd, 5th, 7th):
  2, 3, 6, 15
• Even positions (2nd, 4th, 6th):
  6, 9, 18

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Pattern in Odd Positions (2, 3, 6, 15):

We observe the following:

• 2 → 3: +1
• 3 → 6: ×2
• 6 → 15: ×2.5

So it alternates between +1, ×2, ×2.5…

Let’s continue this pattern:

• 15 → next: +3.5 = 18.5? That seems inconsistent.
  Wait—let’s try another idea:

Look again:

• 2 → 3: ×1.5
• 3 → 6: ×2
• 6 → 15: ×2.5

This is a better fit: each term is multiplied by increasing 0.5 steps.

If this is correct:

• 15 × 3 = 45

So the next in this subsequence is 45.

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Pattern in Even Positions (6, 9, 18):

Let’s look at how these numbers behave:

• 6 → 9: +3 or ×1.5
• 9 → 18: ×2

Try multiplication:

• 6 × 1.5 = 9
• 9 × 2 = 18
  So the multipliers are increasing: ×1.5, ×2

Continue:

• 18 × 2.5 = 45

That’s interesting—same number as before! But wait, this is only the 6th term.

So the pattern continues:

• Even position after 18 → 18 × 2.5 = 45
• Next even: 45 × 3 = 135

But since we alternate, the sequence goes:
Odd: 2, 3, 6, 15, 45
Even: 6, 9, 18, 54, 108

So final combined sequence:

2, 6, 3, 9, 6, 18, 15, 45, 36, 108

Answer: 45, 36, 108
Note: 36 is from 18 × 2 (next even position term).