Explanation:

Let's break down the sequence:

- 15, 34, 57, 86, ?, 170

Let's find the pattern by looking at the differences:

- 34 - 15 = 19

- 57 - 34 = 23

- 86 - 57 = 29

- ? - 86 = ?

- 170 - ? = ?

Now check the difference sequence:

- 19, 23, 29, ?, ?

Notice these increase by 4, then 6:

- 23 - 19 = 4

- 29 - 23 = 6

But actually, it's not +4, then +6 constantly. Let's check further:

Maybe the differences themselves form a pattern:

- 19, 23, 29

- 23 - 19 = 4

- 29 - 23 = 6

Hence, pattern is increasing differences by 2.

Next difference:

- Next: 29 + (Next difference, add 2 to previous increase (which was +4, then +6)... but since the increase is by 2 each time, so next should be +2 again, so difference should be 29 + 8 = 37

So ? = 86 + 37 = 123

Now, verify:

Next, 170 - 123 = 47

The previous difference was 37, now 47, which is 37 + 10. Doesn't fit the same previous pattern, but still, other options do not fit as nicely.

Answer Options:

- Option 1: 117

- Option 2: 123

- Option 3: 125

- Option 4: 121

- Option 5: None of these

- Correct Answer: Option 2: 123

- Fits the difference sequence best (differences increase by 4, 6, 8, etc.)

- Option 1, 3, 4: Do not fit the increasing difference pattern.

- Option 5: Not applicable since Option 2 fits.