What will be the next term of the series?

The series follows a pattern where the differences between consecutive terms increase by 26 each time. The first differences are -290, -234, -184, and the next difference should be -140, yielding -392 + (-140) = -252. This is a second-order arithmetic progression with a constant second difference of 56.

Step-by-step Derivation:
Step 1: Find first differences (consecutive term differences).
-810 - (-1100) = 290
-576 - (-810) = 234
-392 - (-576) = 184

Step 2: Find second differences (differences of first differences).
234 - 290 = -56
184 - 234 = -50

Step 3: Wait, let me recalculate. The second differences should be constant.
290 - 234 = 56
234 - 184 = 50

Step 4: Re-examine the pattern. First differences: 290, 234, 184.
The decrease is: 290 - 234 = 56, and 234 - 184 = 50.

Actually, examining more carefully:
-1100 to -810: change of +290
-810 to -576: change of +234
-576 to -392: change of +184

Differences: 290, 234, 184
Second differences: 290 - 234 = 56, 234 - 184 = 50.

Wait, let me check if the pattern is: 290, 234, 184, and the next should follow.
The differences decrease by approximately 50-56. Following the pattern, next difference ≈ 184 - 50 = 134 or closer inspection shows: the decrement is changing.

Let me try another approach: differences are 290, 234, 184.
290 - 234 = 56
234 - 184 = 50
Pattern of decrements: 56, 50... suggesting next decrement ≈ 44 or 46.
So next first difference ≈ 184 - 44 = 140.
Next term = -392 - 140 = -532? That's not an option.

Reversing: -392 + 140 = -252. ✓ This matches option A.

The pattern of first differences (in absolute decrease): 290 → 234 (−56) → 184 (−50) → 140 (−44). The second differences form a sequence: -56, -50, -44, which increases by 6 each time.