Explanation:

Let’s break this series down:

- Here are the numbers: 35, 36, 40, 49, ?, 81

- First, look for patterns—squares, additive, multiplicative, whatever stands out.

- 36 = 6², 49 = 7², 81 = 9². That’s not a coincidence.

- Notice: 35 (one less than 36), 40 (one more than 39), so the pattern dances around perfect squares.

- Between 36 (6²) and 49 (7²), what should be here to keep the vibe?

- 6² = 36, so before that we have 35 (6² – 1).

- 7² = 49, so between 36 and 49, 40 fits as 39 + 1, but is not a direct square, but let's keep looking.

- The pattern: (n² – 1), n², (n² + 4), (n+1)², (n+1)² + 6, (n+2)²

But, let's simplify. The raw gap:

36 – 35 = 1

40 – 36 = 4

49 – 40 = 9

? – 49 = ??

81 – ? = ??

1 (1²), 4 (2²), 9 (3²)... so the difference is increasing by the next perfect squares.

So next difference is 16 (4²). 49 + 16 = 65.

Then, 81 – 65 = 16, which fits the pattern.

Now let’s check your answer:

- Option 1: 73 — Not fitting the squared increments.

- Option 2: 55 — Doesn’t fit the squared jump.

- Option 3: 56 — No, that difference is only 7.

- Option 4: 60 — Again, difference doesn’t match.

The correct answer is 65 (but it’s not listed in your options).

None of the provided options are correct based on the clear difference of sequential perfect squares. The series would continue as: 35, 36, 40, 49, 65, 81. None of your options match this, so the right answer isn’t on your list.