Question

What is the next number of the following series?
6, 12, 21, 32, ?
(a) 47
(b) 53
(c) 49
(d) 41

Answer 1

Answer:

53 is the right answer b

Answer 2

The required "option (a) 47" is correct.

Step-by-step explanation:

The given sequence:

6, 12, 21, 32, ?

To find, the next number = ?

The pattern follow:

$2^{2}$ + 2, $3^{2}$ + 3, $4^{2}$ + 5, $5^{2}$ + 7, $6^{2}$ + 11,.....

Where, 2, 3, 5, 7, 11 are consecutive prime numbers.

6 = $2^{2}$ + 2 = 4 + 2 = 6

12 = $3^{2}$ + 3 = 9 + 3 = 12

21 = $4^{2}$ + 5 = 16 + 5 = 21

32 = $5^{2}$ + 7 = 25 + 7 = 32

Similarly,

? = $6^{2}$ + 11 = 36 + 11 = 47

∴ The next number (?) = 47

Thus, the required "option (a) 47" is correct.