Find the next in series 4, 16, 64...

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zach9414's profile pic

zach9414 | High School Teacher | (Level 2) Adjunct Educator

Posted on

First of all, with any series problem, we must first decide if it is an arithmetic series or a geometric series. An arithmetic series is one that you can add or subtract to get from the first number to the second. A geometric is like it, but instead of adding and subtracting, we multiply or divide by the same number. 

So looking at these three numbers it gives us, 4, 16, and 64, we can determine what type of series this is.

`16-4=12`

`64-16=48`

So this is not arithmetic since we cannot add or subtract the same number to each value to get the next. 

`16/4=4`

`64/16=4`

Looking at the above values, it appears that to arrive at the next value we just have to multiply the current number by 4.

So to get the 4th term in the series, we just have to multiply 64 times 4

`64*4=256`

Therefore, the 4th term is 256

We can also look at this series as 4 to the nth power 

`4^1 , 4^2 , 4^3 , 4^4`

`4^4=256`

hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

The given series is a geometric series with a common ratio of 4

As 2nd term/1st term = common ratio(r) = 4

Thus, the 4th term is first term*(common ratio)^3 = 4*(4^3) = 256

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