# Math Help - sequences help

1. ## sequences help

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.

2. ## Re: sequences help

Originally Posted by nehal234
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)

$t_n= \frac{3^n}{2^{n-1}}=2 \cdot \left(\frac{3}{2}\right)^n$

3. ## Re: sequences help

thanks but could you show me how you reached that?

4. ## Re: sequences help

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...

5. ## Re: sequences help

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?

6. ## Re: sequences help

$t_1=3$

$t_2=\frac{9}{2}$

$t_3=\frac{27}{4}$

$t_4=\frac{81}{8}$

$\vdots$

7. ## Re: sequences help

i dont see why the base of 2 is being changed.
also how do you out the formulas like how you are doing them?

8. ## Re: sequences help

Originally Posted by nehal234
thanks but could you show me how you reached that?
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)
and 3^n / 2^(n-1) = 2*3^n / 2^n (as per princeps)

Can also be shown as 2^(1-n)3^n

9. ## Re: sequences help

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

10. ## Re: sequences help

Originally Posted by nehal234
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, 6/2
That's NOT a geometric or arithmetic sequence

Arithmetic and Geometric Sequences

11. ## Re: sequences help

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?

12. ## Re: sequences help

could someone help me with part b) of this question?