Question

12,16,20,8,6,10,8,15 what is next number​

Answer 1

The given sequence:

12, 16, 20, 8, 6, 10, 8, 15, ?

We have to find, the value of next number (?).

Solution:

The pattern follow(three numbers):

a, b, c ⇒ $a^{2} +b^{2} =c^{2}$, ....

12 ,16, 20

$12^{2} +14^{2} =20^{2}$

⇒ 144 + 256 = 400

⇒ 400 = 400

8, 6, 10

$8^{2} +6^{2} =10^{2}$

⇒ 64 + 36 = 100

⇒ 100 = 100

Similarly:

8, 15, ?

$?^{2}$ = $8^{2} + 15^{2}$

⇒ $?^{2}$ = 64 + 225

⇒ $?^{2}$ = 289

⇒ $?^{2}$ = $17^{2}$

⇒ ? = 17

∴ Next number (?) = 17

Thus, the value of the next number is 17.

Answer 2

Given:

12,16,20,8,6,10,8,15

To find:

What is the next number​ ?

Solution:

From the given information, we have the data as follows.

The series, 12, 16, 20, 8, 6, 10, 8, 15

We are asked to find the next term of the above series. So, we will continue with the calculation of searching the relation between the terms. So, we have,

The first three terms.

12, 16, 20

12²  + 16² = 20²

144 + 256 = 400

400 = 400

The second three terms.

8, 6, 10

8²  + 6² = 10²

64 + 36 = 100

100 = 100

The third three terms.

8, 15, ?

8²  + 15² = ?²

64 + 225 = ?²

289 = ?²

? = √289

? = 17

∴ The next term of the sequence is 17.