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hey everyone :) im new here and i've got a question which gives me the recursive definition of a sequence and I'm asked to find the nth term.
here it is:
Find a formula for the n-th term tn of the sequence (tn) defined by
a) t1 = 3; tn = 3tn−1/2, n>=2.
the next part is asking me to find the recursive definition of the formula:
b) tn = 2 (n + 1)! 5n, n >=1.
could someone take me through the steps rather than just posting the answer so I can do it myself the next time.
a)Quote:
Originally Posted by nehal234
thanks :) but could you show me how you reached that?
I simply wrote down a few first terms and deduced a general formula...Quote:
Originally Posted by nehal234
i've tried to input values into n such as 1 2 3 etc and i dont get the same values as if i put tn=1 2 3 etc
t1=3
t2=3/2
t3=6/2
t4=9/2
is there something im dong wrong?
i dont see why the base of 2 is being changed.
also how do you out the formulas like how you are doing them?
Quote:
Originally Posted by nehal234
and 3^n / 2^(n-1) = 2*3^n / 2^n (as per princeps)Code:1 2 3 4 ......... n
3 (3/2) 9/2 (3/2) 27/4 (3/2) 81/8 ......... (3/2) 3^n/2^(n-1)
Can also be shown as 2^(1-n)3^n
i belive what the sequence means is that t1=3 then t2=(3*1)/2 and t3=(3*2)/2
so i dont know how 27/4 81/8 and all of them come from
so you "think" 1st three terms are: 3, 3/2, 6/2Quote:
Originally Posted by nehal234
That's NOT a geometric or arithmetic sequence
Arithmetic and Geometric Sequences
Couldn’t find any other suitable topic for my question :)
I was looking at a roulette tips and tricks page but I couldn’t find any maths sequence related advice. Can anyone please help me to determine what the roulette algorithms are and how maths can be applied to roulette? I know that there’s not special system, however I’m sure maths can resolve some probability questions in roulette?
could someone help me with part b) of this question?