Answer:
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
