Explanation:

Let’s break down this sequence:

11, 13, 19, 49, 109, 239, ?

- First, look for the pattern in how each number changes.

- 13 - 11 = 2

- 19 - 13 = 6

- 49 - 19 = 30

- 109 - 49 = 60

- 239 - 109 = 130

Now, let's compare the differences:

2, 6, 30, 60, 130

Do you notice how each difference doubles and then adds 2?

- 2 × 2 + 2 = 6

- 6 × 5 + 0 = 30 (wait, not quite doubling—looks like a multiplying pattern, not just addition)

- 30 × 2 = 60

- 60 × 2 + 10 = 130

But if you look again, each difference is roughly multiplying by 2:

- 2

- 2 × 3 = 6

- 6 × 5 = 30

- 30 × 2 = 60

- 60 × 2 + 10 = 130

Or maybe it's really just 2, 6, 30, 60, 130—hmm.

Here's a better look. Check the ratio between differences:

- 6/2 = 3

- 30/6 = 5

- 60/30 = 2

- 130/60 ˜ 2.17

That's not a perfect pattern, so let's see what happens if the next difference is around double the previous one:

- 130 × 2 = 260

So, 239 + 260 = 499. That’s not any given option.

Let's see what happens with each option:

- Option 1: 449 ? Difference: 449 - 239 = 210

- Option 2: 494 ? 494 - 239 = 255

- Option 3: 394 ? 394 - 239 = 155

- Option 4: 349 ? 349 - 239 = 110

Now, does 130 to 210 follow any stable pattern?

If you look back:

2, 6, 30, 60, 130, 210...

It’s close to being approximately double each time, but the actual pattern seems to be:

2 × 3 = 6

6 × 5 = 30

30 × 2 = 60

60 × 2 + 10 = 130

130 × 1.615 = 210

Doesn’t fit perfectly, but 449 is the only option that follows a near doubling of the difference.

So, the answer that makes most sense given these options is:

Option 1: 449