Sequences: sequence given by T_n = 3(2/3)^n - 1, where n is a positive integer; find T_1,T_2,T_3; show that T_{n+1) = 2(2/3)^n - 1; and

[reggiwilliams]

Revising Sequences
Came across attached question and can do part one but struggling with parts 2 & 3
Can anyone guide me on how to approach?

 

[BigBeachBanana]

Revising Sequences
Came across attached question and can do part one but struggling with parts 2 & 3
Can anyone guide me on how to approach?

2) To find [imath]T_{n+1}[/imath], replace [imath]n[/imath] with [imath]n+1[/imath] in [imath]T_n[/imath], then simplify.

3) Substitute the expressions for [imath]T_n[/imath] and [imath]T_{n+1}[/imath] then simplify.

 

[reggiwilliams]

Think I have it part three k = -1
Is that correct
Part one I made answers 1,1/3 and -1/9 but looking at it worry because no common ratio
As question does not state it is an geometric sequence needn’t worry

 

[BigBeachBanana]

Think I have it part three k = -1
Is that correct
Part one I made answers 1,1/3 and -1/9 but looking at it worry because no common ratio
As question does not state it is an geometric sequence needn’t worry

I have the same answer. However, -1 does not belong to the natural numbers as stated.