Question Discussion & Solution

The pattern of the series is

6 × 3 + 1 = 19

19 × 3 + 2 = 59

59 × 3 + 3 = 180

180 × 3 + 4 = 544

544 × 3 + 5 = 1637 

The series follows the following pattern:

45 + 3² = 54

54 + 4² = 70

70 + 5² = 95

95 + 6² = 131

131 + 7² = 180

CALCULATIONS:

225 ÷ 3 = 75

75 ÷ 2.5 = 30

30 ÷ 2 = 15

15 ÷ 1.5 = 10

10 ÷ 1 = 10

10 ÷ 0.5 = 20

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

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.