Question Discussion & Solution

CALCULATIONS:

21² - 21 = 441 - 21 = 420

22² - 22 = 484 - 22 = 462

23² - 23 = 529 - 23 = 506

24² - 24 = 576 - 24 = 552

25² - 25 = 625 - 25 = 600

26² - 26 = 676 - 26 = 650

The pattern followed in this question is:

8² + 8 = 72

9² + 9 = 90

10² + 10 = 110

11² + 11 = 132

12² + 12 = 156

Calculation∶

The series follows the following pattern

11 + 8 = 19 → 2³

19 + 9 = 28 → 3²

28 + 64 = 92 → 4³

92 + 25 = 117 → 5²

117 + 216 = 333 → 6³

∴ The missing term in the series is 117.

Logic: Alternate Cube and Square of consecutive numbers.

The pattern followed by the series is

234 + 4 = 238

238 + 14 = 252

252 + 24 = 276 

276 + 34 = 310 

310 + 44 = 354 

Calculation:

The given series is the cube of prime numbers

2³ = 8

3³ = 27

5³ = 125

7³ = 343

11³ = 1331

13³ = 2197

∴ The value of ? is 343.