Explanation:

Let’s break this down:

- The series is: 16, 35, ?, 217, 653, 1309

- Let's look for a pattern between the numbers.

Here's what stands out:

- 16 to 35 is an increase of 19

- 35 to ? (let's call this x) = x - 35

- x to 217 = 217 - x

- 217 to 653 is an increase of 436

- 653 to 1309 is an increase of 656

Let’s try factoring or powers:

- 16 = 24

- 35 = (3³) + 8

- 217 = (6³) + 81

None of the exponents/powers seem to fit a simple pattern.

But try this:

- The difference doubles then adds 2.

16 to 35 = 19

35 to ? = d

? to 217 = bigger gap

But, that’s messy.

Try ratios:

16 × 2 + 3 = 35

35 × 3 + 4 = 109

But 109 isn’t among the options, nor does it fit in the series. Let’s look at cube numbers:

2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512

But the given numbers are close to these cubes.

Let’s check, say:

- 16 (2³ + 8)

- 35 (3³ + 8) -- but that's 27 + 8 = 35

- Next, try (4³ + 8) = 64 + 8 = 72

So, the pattern: n³ + 8

So:

n = 2: 8 + 8 = 16

n = 3: 27 + 8 = 35

n = 4: 64 + 8 = 72

n = 5: 125 + 8 = 133

n = 6: 216 + 1 = 217

So, the missing value should be 72.

Let’s see the options:

Option:1, 72

Option:2, 128

Option:3, 77

Option:4, 107

The answer is Option 1: 72.

- Option 1 (72) fits the pattern perfectly (n³+8 for each n from 2 upwards.)

- Option 2 (128) doesn’t fit with the rest.

- Option 3 (77) is not in the cubic plus formation.

- Option 4 (107) is not in the sequence logic.

What this really means is: The next number is 72. Option 1 is the only possible answer.