Help with mathematical induction and sequences

[livah]

Hello there! There is a problem I have which I can't get right no matter what.

A sequence is defined recursively with the first element a₁ = 2 and a_n+1 = 3 * a_n - 2. Prove by means of mathematical induction that a_n = 3^n-1 + 1.

I keep getting that a_n+1 = 3 * a_n. Please help!!! This is driving me insane

 

[stapel]

Hello there! There is a problem I have which I can't get right no matter what.

A sequence is defined recursively with the first element a₁ = 2 and a_n+1 = 3 * a_n - 2. Prove by means of mathematical induction that a_n = 3^n-1 + 1.

I keep getting that a_n+1 = 3 * a_n.

Please reply showing your work, so we can see where things are going astray. Thank you!

 

[JeffM]

Hello there! There is a problem I have which I can't get right no matter what.

A sequence is defined recursively with the first element a₁ = 2 and a_n+1 = 3 * a_n - 2. Prove by means of mathematical induction that a_n = 3^n-1 + 1.

I keep getting that a_n+1 = 3 * a_n. Please help!!! This is driving me insane

You do understand, I hope, that a proof by induction of a proposition dependent
on n requires FIRST proving the proposition true for n = 1.

Can you take that first step?