Question

Which numbers will replace the question mark? in following series 5,9,18,43,93,213,382,?

Answer 1

Answer:

Step-by-step explanation:

Consider the provided series.

5, 9, 18, 43, 92, 213, 382, ?​

Observe the pattern.

Here the pattern is, the difference between the term is the square of next prime number.

9-5 = 4 = (2)² ------- 2 is the first prime number.

18-9 = 9 = (3)² ------- 3 is the second prime number.

43-18 = 25 = (5)² ------- 5 is the third prime number.

92-43 = 49 = (7)² ------- 7 is the 4th prime number.

213-92 = 121= (11)² ------- 11 is the 5th prime number.

382-213 = 169= (13)² ------- 13 is the 6th prime number.

Hence, the next difference should be 289 = 17² as 17 is the 7th prime number.

382+289=671

Hence, the next number should be 671.