Explanation:

To solve the number series, let's identify the pattern:

- The sequence starts with 77 and then decreases by 1 to 76.

- Next, it jumps to 84, which is an increase of 8.

- From 84, it drops significantly to 57, which is a decrease of 27.

- We need to find the next number before reaching -4.

Let's analyze the pattern:

- First Move: 77 to 76 is a decrease of 1.

- Second Move: 76 to 84 is an increase of 8.

- Third Move: 84 to 57 is a decrease of 27.

Notice the pattern alternates between decrease and increase, and the amount of change itself alternates in a particular manner:

- Increase: -1, +8, -27, ?

- Looks like a pattern of alternating signs and growing steps (1×(1)^2, 2×(2)^2, 3×(3)^2, 4×(4)^2).

Continuing this pattern:

- Fourth Move: From 57 to the next number:

- It should be an increase by 4×(4)^2 = 4×16 = 64.

- Result: 57 + 64 = 121

Reviewing Options:

- Option 1: 81

- Option 2: 100

- Option 3: ? 121 (Correct Answer)

- Option 4: 144

- Option 5: 169

Therefore, the correct answer is 121.