Can anyone pls slove this number sequence?

Question

Pls slove 8,4,1,1/3,___,___
Pls give me what is the nth term also pls

Answer 1

Hi,

The equation for this sequence is

u(n) = 2/9n³ + 5/6n² - 55/18n + 35/3

The next 2 terms are 10/3 and 34/3.

I got this by entering this data into STAT on my calculator as y values for 1,2,3, and 4.

I hope that helps!! :-)

Answer 2

There are lots of solutions.

Each term can come from dividing the previous term by a small whole number. These numbers are 4, 2, 3, ...

So the question is now, how does that sequence continue? But nobody can know. There is the possibility 4, 2, 3, 4, 2, 3, 4, ... but it is not the only one.

But instead of dividing, each term in 8, 4, 1, 1/3 ... can come from subtracting a number from the previous term. These numbers are 4, 3, 2/3, ... and when we write them as fractions they are 4/1, 3/1, 2/3, ... The numerators go 4, 3, 2, ... so it is easy to see how that continues. But the denominators go 1, 1, 3, ... and it is not easy to decide how to continue that. Take each term plus twice the next? That would be 1, 1, 3, 7, 17, 41, ...so the subtraction numbers become 4/1, 3/1, 2/3, 1/7, 0/17, -1/41 ... and the whole series is 8, 4, 1, 1/3, 4/21, 4/21, 185/861, ... But there are other possible ways to continue the sequence 1, 1, 3, ... so we still do not know.