i have just started my OU course and am struggling to get to terms with the geometric sequences, i believe i cannot post the actual question on here, but was wondering if anyone can help me with explaining how i can find a closed form, i have a regular pattern of deducting 0.7 from each previous answer, so i know it is an arithmetic sequence, but just cannot get to grips with the closed form
cheers guys
trace
I guess I am a little confused about your question. First you state that it is a geometric series. This means you are multiplying by the same ratio every time an example would be
Where the common ratio and your starting value is .
So I guess my question for you is when you say
By decucting do you mean subtraction or are you multiplying byi have a regular pattern of deducting 0.7 from each previous answer
If you are multiplying the geometric series should look like
Or is the sum is finite you would get
P.S what is OU?
i said geometric series, as that what is comes under i think? the open university(OU) states that i cannot display my questions,and i don't want to cheat at all, hence why i asked for help with how to figure it out
i have done a lot of reading it is an arithmetic sequence, that starts from 3.2 and follows decreases by 0.7 each time, (starts at 3.2)
i have found the recurrent system to descrtibe it, however i am struggling to find the closed form 4 this.
I have been pickling it for ages and the closest i get is :
3.2=(Un-1)0.7
or Un=3.2-(0.7)n-1
hope this is a bit clearer, cheers
Actually, that makes it less clear! You now talk about "arithmetic sequence" as well as "geometric series and also talk about "recurrence" when neither of those last equations is a recurrence relation! The first does not have a " and the second does not have a .
For a geometric sequence, , where each term is the previous term multiplied by a constant, your recurrence relation would be img.top {vertical-align:15%;} with and the closed form
For an arithmetic sequence, , where each term is the previous term with a constant, d, added, your recurence relation would be . Here that would be [maht]U_n= U_{n-1}- 0.7" alt="U_n= rU_{n-1}. Here that would be with and the closed form
For an arithmetic sequence, , where each term is the previous term with a constant, d, added, your recurence relation would be . Here that would be [maht]U_n= U_{n-1}- 0.7" /> and and the closed form .
A "series" would be a sum of those things.
cheers for the help hallsofivy, yeah sorry for the confusion, it was an arithmetic sequence. What i got confused on is my next one is a geometric sequence, which i need to find the first four terms and a closed sequence for, if i show you the sequence can you not tell me the answer please but just some guidance on how i should be working it out, cos never seen this sort of geometric sequence before.
u1=5, un+1=0.4un (n=1,2,3....)
many thanks
trace