find the general term that describes the following sequens
600,300,150,75
I the thing is that you divide each of them by 2
so I would go
y(n)= 600/ 2^n
but how do I check if this is right?
is this right?
It is right.
That would certainly be a good guess, and 'a' possible sequence. It would be the most natural one to use too in my opinion.
How to test it?
You're hypothesizing that the general or nth term is 600/2n so for n=1 you'd have
600/2 = 300, so you might want to alter the general term to be
600/2n-1 then for n=1 you'd have
600/21-1 = 600/20 =600/1 = 600
For n=2 you'd have 600/21 = 300
Then y(n) would be right for the first 4 terms of the sequence.
To confirm if your general term is correct, you can test it by plugging in the values of n and checking if the resulting terms match the given sequence.
For the given sequence: 600, 300, 150, 75
Using the general term you proposed: y(n) = 600/2^n
Let's test it:
For n = 1: 600/2^1 = 600/2 = 300 (matches the second term of the sequence)
For n = 2: 600/2^2 = 600/4 = 150 (matches the third term of the sequence)
For n = 3: 600/2^3 = 600/8 = 75 (matches the fourth term of the sequence)
Since your general term produces the correct terms for the given sequence, it is likely that you have found the correct general term.