Question Discussion & Solution

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

CALCULATIONS:

225 ÷ 3 = 75

75 ÷ 2.5 = 30

30 ÷ 2 = 15

15 ÷ 1.5 = 10

10 ÷ 1 = 10

10 ÷ 0.5 = 20

The pattern followed in this question is:

8² + 8 = 72

9² + 9 = 90

10² + 10 = 110

11² + 11 = 132

12² + 12 = 156

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.

Considering the above series-

295, 286, 268, 241, 205, ?

The logic of the series can be explained as,

295 – 9 = 286

286 – 18 = 268

268 – 27 = 241

241 – 36 = 205

By observing the pattern, we can write

205 – 45 = 160

⇒ ? = 160

∴ The value of ? is 160.