Read the numbers and decide what the next number should be: 6 18 20 10 30 32 16.

Number series are the sequences in which the terms follow a particular pattern by virtue of which the series progresses further. The solver is required to identify the pattern to solve the problem.

Answer: The next number in the sequence 6 18 20 10 30 32 16 is 48.

Let's understand the solution in detail.

Explanation:

We are given the pattern: 6, 18, 20, 10, 30, 32, 16, __

Here, we have to identify the progression of the series to solve the problem.

So, here we can notice the following pattern:

• The first number is multiplied by 3, which gives the next number, that is, 6 × 3 = 18.
• Then, 2 is added to the second number to give the third number, that is, 18 + 2 = 20.
• Then, the third number is divided by 2 to give the fourth number, that is, 20 / 2 = 10.
• Then again,10 is multiplied by 3 to give 10 × 3 = 30 (Same as the 1st step).
• Then, 2 is added to 30 to give 30 + 2 = 32 (Same as the 2nd step).
• Then, 32 is divided by 2 to give 32 / 2 = 16 (Same as the 3rd step).

With the help of the above observations, we can see that the pattern is multiplying by 3, then adding 2 to the answer, and then dividing it further by 2, and this pattern repeats.

Therefore, the next number will be 16 × 3 = 48.

Hence, the next number in the sequence 6, 18, 20, 10, 30, 32, 16 is 48.