In each series one term is wrong. You have to find the wrong term of the…

Concept

In a wrong-number series, every term is generated from the previous one by a single fixed rule and exactly one term violates that rule. The method is to compute the consecutive differences and test them against a recognisable sequence — here the differences turn out to be the squares of consecutive prime numbers.

Application

Take the differences between successive terms of 8, 129, 298, 587, 950, 1477, 2318:

1. 129 − 8 = 121 = 112

2. 298 − 129 = 169 = 132

3. 587 − 298 = 289 = 172

4. the next gap must be 192 = 361, giving 587 + 361 = 948

5. 1477 − 948 = 529 = 232

6. 2318 − 1477 = 841 = 292

The intended pattern adds the squares of the consecutive primes 11, 13, 17, 19, 23, 29. Five of the six gaps match exactly. The only break is at the fifth term: the series shows 950, but the prime-square rule requires 587 + 361 = 948. So 950 is the term that does not belong.

Cross-check

Rebuild the series with 948 in place of 950: 8, 129, 298, 587, 948, 1477, 2318. The differences are then exactly 121, 169, 289, 361, 529, 841 — the squares of 11, 13, 17, 19, 23, 29 with no exception. This confirms 950 (which should be 948) is the wrong term.