Find the wrong number in the series given below: 28, 84, 112, 196, 308, 504, 872

Concept

In an additive recurrence series, each term after the first two is obtained from the two immediately preceding terms. To locate an erroneous term, compute the expected value at every later position and compare it with the listed value.

Application

1. The first check gives 28 + 84 = 112.

2. The next check gives 84 + 112 = 196.

3. Continuing gives 112 + 196 = 308.

4. Then 196 + 308 = 504.

5. For the last place, 308 + 504 = 812, whereas the series lists 872.

Cross-check

Working backward also confirms the chain: 504 − 308 = 196, 308 − 196 = 112, 196 − 112 = 84, and 112 − 84 = 28. Thus the consistent final value is 812, so the wrong listed number is 872.