Sequences: find formula for n-th term of t_1=2, t_n=(4t_{n-1})/3, n>=2

[itsmak98]

How to solve these Sequence questions?

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(a) Find, showing all working, a formula for the n-th term t_n of the sequence (t_n) defined by

. . . . .\(\displaystyle t_1\, =\, 2;\quad t_n\, =\, \dfrac{4t_{n-1}}{3},\quad n\, \geq\, 2\)

(b) Find, showing all working, a recursive definition for the sequence with general term

. . . . .\(\displaystyle t_n\, =\, 5\, (n\, +\, 1)!\, 2^{n-1},\quad n\, \geq\, 1\)

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I can't I've tried so many times!

 

[Deleted member 4993]

How to solve these Sequence questions?

---

(a) Find, showing all working, a formula for the n-th term t_n of the sequence (t_n) defined by

. . . . .\(\displaystyle t_1\, =\, 2;\quad t_n\, =\, \dfrac{4t_{n-1}}{3},\quad n\, \geq\, 2\)

(b) Find, showing all working, a recursive definition for the sequence with general term

. . . . .\(\displaystyle t_n\, =\, 5\, (n\, +\, 1)!\, 2^{n-1},\quad n\, \geq\, 1\)

---

I can't I've tried so many times!

t_n = 4/3 * t_(n-1)

= (4/3)^2 * t_(n-2)

= (4/3)^3 * t_(n-3)

continue...

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

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http://www.freemathhelp.com/forum/announcement.php?f=33

 

[stapel]

How to solve these Sequence questions?

---

(a) Find, showing all working, a formula for the n-th term t_n of the sequence (t_n) defined by

. . . . .\(\displaystyle t_1\, =\, 2;\quad t_n\, =\, \dfrac{4t_{n-1}}{3},\quad n\, \geq\, 2\)

(b) Find, showing all working, a recursive definition for the sequence with general term

. . . . .\(\displaystyle t_n\, =\, 5\, (n\, +\, 1)!\, 2^{n-1},\quad n\, \geq\, 1\)

---

I can't I've tried so many times!

Great! Then you've got plenty that you can show us!

Please reply showing us your thoughts and efforts for at least one attempt on each of these exercises. Thank you!