What is the next number 3, 6, 4, 8, 6, 12, 10, ...?

Solution:

Series is solved using the relation between the consecutive terms.

Given series: 3, 6, 4, 8, 6, 12, 10, ...

Relation between 1^st number and 2^nd number = 1^st number × 2 = 2^nd number

Difference between 3^rd number and 2^nd number = 4 - 6 = -2

Relation between 3^rd number and 4^th number = 3^rd  number × 2 = 4^th number

Difference between 5^th number and 4^th number = 6 - 8 = -2

Relation between 5^th number and 6^th number = 5^th number  × 2 = 6^th number

Difference between 7^th number and 6^th number = 10 - 12 = -2

Relation between 7^th number and 8^th number = 7^th number × 2 = 8^th number 

⇒ 8^th number = 7^th number × 2 = 10 × 2 = 20

So, 8^th term is 20

Therefore, the final term of the series will be 20.

What is the next number 3, 6, 4, 8, 6, 12, 10, ...?

Summary:

The final term of the series will be 20.