Explanation:

Let's break the pattern of the series: 30, 39, 55, 76, ?

- Difference between 39 and 30 = 9

- Difference between 55 and 39 = 16

- Difference between 76 and 55 = 21

Now, look at the pattern in the differences: 9, 16, 21

- 9 = 3²

- 16 = 4²

- 21 = (not a perfect square, but next expected would be 25, i.e., 5²)

So, let's add 25 to 76:

76 + 25 = 101

But 101 is not among the options. Let's check if another pattern fits.

Check the differences more closely.

- 39 - 30 = 9

- 55 - 39 = 16

- 76 - 55 = 21

Notice:

- 9 (+7), 16 (+5), 21

The differences themselves increase by -2 each time:

16 - 9 = 7

21 - 16 = 5

So, next difference should be 21 + 3 = 24 (since 7, 5, next should be 3 less, i.e., 3).

But if we follow the perfect square logic for a moment:

- 9 (3²)

- 16 (4²)

- the next square would be 25 (5²), then 36 (6²), but 21 is not a square.

Try skipping by adding increasing numbers: Differences: +9, +16 (+7), +21 (+5), next should be +24 (+3).

76 + 24 = 100

Now, let's check the options:

1. 97

2. 100

3. 87

4. 91

Correct Answer: 100

Summary:

- The sequence adds 9, 16, 21, 24. The differences increase by 7, 5, 3.

- The most logical next number is 24, giving 100.