Question Discussion & Solution

7 × 2 – 2 = 12

12 × 3 – 3 = 33

33 × 4 – 4 = 128

128 × 5 – 5 = 635

Given:

2, 10, 18, 54, 162, 486, 1458

Calculation:

The pattern of the number series is:

2 × 3 = 6 ≠ 10

6 × 3 = 18

18 × 3 = 54

54 × 3 = 162

∴ 10 is Wrong Number

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.

Given series:

5, 15, 50, ?, 1030, 6185

Calculation:

The series is following the below pattern,

5 × 2 + 5 = 15

15 × 3 + 5 = 50

50 × 4 + 5 = 205

205 × 5 + 5 = 1030

1030 × 6 + 5 = 6185

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.