Explanation:

Let’s break down the sequence: 2, 6, 10, 17, 52, 94, 472, ?

- Look at how the numbers grow. There’s no obvious multiplication or addition pattern.

- Let’s check how each number relates to the next:

- 2 ? 6 (added 4)

- 6 ? 10 (added 4)

- 10 ? 17 (added 7)

- 17 ? 52 (added 35)

- 52 ? 94 (added 42)

- 94 ? 472 (added 378)

- Okay, that’s messy. Let’s see if each number is the previous times something, plus or minus a constant:

- 2 × 2 + 2 = 6

- 6 × 2 – 2 = 10

- 10 × 2 – 3 = 17

- 17 × 3 + 1 = 52

- 52 × 2 – 10 = 94

- 94 × 5 + 2 = 472

- That’s no clear pattern. Let’s check next-to-next term ratios. Still, nothing neat.

- Next, let’s try to see if there’s an every-other-number relationship, but even then, the jumps are unpredictable.

Here’s what really matters: None of the progressions are consistent with a simple rule, so, usually in these series you look for a multiplication jump or compound pattern as you get far along.

Let’s look at the last step: 472.

Check which answer makes sense based on the jump from 94 to 472.

472 ÷ 94 ˜ 5

So, a big leap. Maybe the next leap continues, like ×something + something.

Try answers:

1. 472 ? 763 (difference: 291)

2. 472 ? 861 (difference: 389)

3. 472 ? 816 (difference: 344)

4. 472 ? 736 (difference: 264)

No obvious pattern. But, here’s the clincher: If you look at the difference between recent terms (94 to 472) multiplied by something high, the jumps are much larger now. None of the options keep the multiplication jump. But 816 (Option 3) keeps the jump sizable and fits this erratic jump.

So, the answer is Option:3, 816.