Question Discussion & Solution

The pattern followed in this question is:

0² + 3 = 3

1² + 4 = 5

2² + 5 = 9

3² + 6 = 15

4² + 7 = 23

The number pattern in the series can be decoded as:

⇒ 3

⇒ 4 – 3 = 1 = 1⁴

⇒ 20 – 4 = 16 = 2⁴

⇒ 101 – 20 = 81 = 3⁴

⇒ 357 – 101 = 256 = 4⁴

⇒ 982 – 357 = 625 = 5⁴

⇒ 2278 – 982 = 1296 = 6⁴

The series follows the following pattern:

12 × 1 + 1 = 13

13 × 2 + 1 = 27

27 × 3 + 1 = 82

82 × 4 + 1 = 329

329 × 5 + 1 = 1646

The series follows the following pattern:

45 + 3² = 54

54 + 4² = 70

70 + 5² = 95

95 + 6² = 131

131 + 7² = 180

The series follows the following pattern:

346 - 22 = 342

342- 32 = 333

333 - 52 = 308

308 - 72 = 259

259 - 112 = 138

∴ The wrong term in the series is 178.