Discussion
Which one of the following options is correct for the given data in the table?
| Iteration (i) | 0 | 1 | 2 | 3 |
| Input (I) | 20 | -4 | 10 | 15 |
| Output (X) | 20 | 16 | 26 | 41 |
| Output (Y) | 20 | -80 | -800 | -12000 |
Answer: A
The relations are X(i) = X(i - 1) + I(i) and Y(i) = Y(i - 1) I(i), for i > 0.
Check X: 20 + (-4) = 16, 16 + 10 = 26, 26 + 15 = 41. Each output adds the new input to the previous output.
Check Y: 20 × (-4) = -80, -80 × 10 = -800, -800 × 15 = -12000. Each output multiplies the previous output by the new input.
The option with X multiplying would give 20 × (-4) = -80 for X(1), not 16, and Y adding would give 16, not -80. The last option multiplies Y by the previous input, giving Y(1) = 20 × 20 = 400 instead of -80.
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