4, 12, 16, 48, 64, 192,
next number in the series?
i tried 4 x 3, + 4, x 3, + 4 but stopped working at 48.

The next term in the series is 256

Step-by-step explanation:

Lets explain how to solve the problem

The series is:

4 , 12 , 16 , 48 , 64 , 192

If we subtract 12 - 4 = 8

If we subtract 16 - 12 = 4

The difference is not constant then it's not an arithmetic series

If we divide 12 by 4 the answer is 3

If we divide 16 by 12 the answer is 4/3

The ratio is not constant then it's not a geometric series

So lets look to the odd positions 1st , 3rd , 5th, they are:

4 , 16 , 64

16 ÷ 4 = 4

64 ÷ 16 = 4

There is a constant ratio 4 between each 2 consecutive odd position

terms

Lets look to the even positions 2nd , 4th , 6th, they are:

12 , 48 , 192

48 ÷ 12 = 4

192 ÷ 48 = 4

There is a constant ratio 4 between each 2 consecutive even position

terms

Now we can find any term is the series by multiply the previous odd

position by 4 if the term in odd position and multiply the previous

even position by 4 if the term in even position

The next term is in the 7th position, then the next term is:

The number in the 5th position × 4

∵ The number in the 5th position is 64

∴ The number in the 7th position = 64 × 4 = 256

* The next term in the series is 256