Explanation:

Let’s break this down step by step:

- First, look at the pattern in the series: 10, 14, 31, 35, 73, 77, ?

- Notice that the numbers seem to jump in bigger increments, then small ones. There’s a clear +4, then a jump of +17, then +4, then +38, and so on.

- Now, let’s lay out the differences:

- 14 - 10 = 4

- 31 - 14 = 17

- 35 - 31 = 4

- 73 - 35 = 38

- 77 - 73 = 4

- ? - 77 = ??

- The pattern: +4, +17, +4, +38, +4, ?

- It looks like every other number is +4, while the numbers in between (+17, +38) are increasing—but how?

- 17 and 38: 38 is 21 greater than 17. Let’s see if that pattern continues.

- So, if we add 21 to 38, we get 59.

- That means the next bigger jump should be 77 + 59 = 136.

- But wait: in this alternating pattern, we do the +4 first, then the big jump.

- 73 + 4 = 77, so next comes the bigger jump: 77 + 59 = 136.

Now, let’s compare that to the options:

- Option 1: 154 – nope, doesn’t fit the pattern.

- Option 2: 90 – too small.

- Option 3: 157 – nope.

- Option 4: 81 – that would be 77 + 4, but based on the alternation, +4 already happened, so now we need the big jump.

Here’s the thing: 136 should be the correct answer, but it’s not even in your choices. Let’s double-check:

- Series: 10, 14(+4), 31(+17), 35(+4), 73(+38), 77(+4), ?

- Expected: 77 + 59 = 136. None of the given options match that exactly.

- But, if you thought it should be 157 (option 3), that would mean a difference of 80, which doesn't match a progression pattern we see.

So, here’s my takeaway:

The series is meant to be: add 4, add increasing number (by 21 each time), repeat. Next jump is +59, so the answer should be 136—but none of your options are correct.

If you want one that sort of makes sense, 81 (option 4) continues the +4 alternate, but by the pattern, it’s not next in line. None fit perfectly. If this was a real-world exam question, I’d mark 136 if it was there! But as per your options: none are correct; 136 would be it.