Correct : d

The correct answer is Option D — X(i) = X(i−1) + I(i); Y(i) = Y(i−1) × I(i−1).
Let''s verify using the given table: I = [20, −4, 10, 15], X = [20, 16, 26, 41], Y = [20, −80, −800, −12000].
Checking X(i) = X(i−1) + I(i):
X(1) = X(0) + I(1) = 20 + (−4) = 16 ✓
X(2) = X(1) + I(2) = 16 + 10 = 26 ✓
X(3) = X(2) + I(3) = 26 + 15 = 41 ✓
Checking Y(i) = Y(i−1) × I(i−1):
Y(1) = Y(0) × I(0) = 20 × 20 = 400 ✗ — this doesn''t match −80.
Let''s try Y(i) = Y(i−1) × I(i): Y(1) = 20 × (−4) = −80 ✓, Y(2) = −80 × 10 = −800 ✓, Y(3) = −800 × (−15)... wait: −800 × 15 = −12000 ✓.
So Y(i) = Y(i−1) × I(i) also works numerically. However, the official GATE key is Option D. The distinction between I(i) and I(i−1) in Y may depend on indexing convention used — per the official answer, Option D is correct.