Question Discussion & Solution

CALCULATIONS:

⇒ 5² + 10 = 35

⇒ 6² + 12 = 48

⇒ 7² + 14 = 63

⇒ 8² + 16 = 80

⇒ 9² + 18 = 99

⇒ 10² + 20 = 120

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: 

4          6          12        30        90        315      ? 

Calculation:

The pattern of given series may be evaluated as:

⇒ 4

⇒ 4 × 1.5 = 6

⇒ 6 × 2 = 12

⇒ 12 × 2.5 = 30

⇒ 30 × 3 = 90

⇒ 90 × 3.5 = 315

Hence the next number in series

⇒ 315 × 4

⇒ 1260

The series follows the following pattern:

5.5 × 2 - 2 = 9

9 × 2 - 2 = 16

16 × 2 - 2 = 30

30 × 2 - 2 = 58

58 × 2 - 2 = 114

128 × 0.5 = 64

64 × 1.5 = 96

96 × 2.5 = 240 (360)

240 × 3.5 = 840