Explanation:

Let’s break it down:

- Here’s the series: 17, 20, 80, 85, ?, 517

- Looking for a pattern, let's look for alternates:

- 17 to 20: +3

- 20 to 80: +60

- 80 to 85: +5

- 85 to ?: ?

- ? to 517: ?

- See the trend? The jumps alternate: small increase (+3), big increase (+60), small (+5), then the next should be a big jump to keep the pattern.

- So, let's check the jump from 85 to the options:

- Option 1: 412 ? 412-85 = 327

- Option 2: 213 ? 213-85 = 128

- Option 3: 504 ? 504-85 = 419

- Option 4: 510 ? 510-85 = 425

- Next, 517-? should be a small step, like +3 and +5 before.

Let’s test these quickly:

- If we use 504 (Option 3), then 517-504 = 13 — that's a fairly small step, fits the pattern of small jumps after big ones.

- If we use 510 (Option 4), then 517-510 = 7 — even smaller, also fits the pattern.

But, the series alternates between additions: +3, +60, +5, +419, +13

Here’s what really makes it click:

- The differences: +3, +60, +5, +419, +13. The big jumps (60 and 419) and the small ones (3, 5, 13). The big jump after +5 should correspond with option 3’s +419 (504-85=419), then +13 to reach 517.

So... the correct answer is Option 3: 504