Question Discussion & Solution

The pattern followed by the series is

234 + 4 = 238

238 + 14 = 252

252 + 24 = 276 

276 + 34 = 310 

310 + 44 = 354 

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 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.

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:

32 × 0.5 = 16

16 × 1.5 = 24

24 × 2.5 = 60

60 × 3.5 = 210

210 × 4.5 = 945

∴ The missing term in the series is 32.