Year 2 Pure Maths - Mixed exercise 3 Q4c

I'm just a bit consufed on how to get the answer to Q4c in the Year 2 Pure Maths book in chapter 3, mixed exercise 3 - Q4C. Would someone be able to explain the steps to me, as I don't really understand the solution on solutionbank.
Thank you!

Is this the one where you're asked to prove a relationship between $u_{n+1}$ and $u_n$?

Start by writing down an expression for each one using the definition you're given earlier.

Yeah sort of, well it just says about writing down a recurrence relation from a given sequence formula and prove that the recurrence relation matches that formula, I attached an image to the post so you can see it.

Is this the one where you're asked to prove a relationship between $u_{n+1}$ and $u_n$?

Start by writing down an expression for each one using the definition you're given earlier.

Yes, so what have you done?

Write down the definition of $u_n$ from the formula they've given you.

Now write down what $u_{n+1}$ is equal to using the same formula.

Now can you show that the relationship they've asked you to prove is true by manipulating these formulae?

I'm just a bit consufed on how to get the answer to Q4c in the Year 2 Pure Maths book in chapter 3, mixed exercise 3 - Q4C. Would someone be able to explain the steps to me, as I don't really understand the solution on solutionbank.
Thank you!

Is this the one where you're asked to prove a relationship between $u_{n+1}$ and $u_n$?

Start by writing down an expression for each one using the definition you're given earlier.

Yes, so what have you done?

Write down the definition of $u_n$ from the formula they've given you.

Now write down what $u_{n+1}$ is equal to using the same formula.

Now can you show that the relationship they've asked you to prove is true by manipulating these formulae?

I don't know how they approached this in the solution bank, but what I would suggest is:

1) Start with the given expression for u_n and rearrange it to make (2/3)^n the subject.

2) Move on to the expression for u_(n+1), based on the expression for u_n. Substitute in the expression for (2/3)^n you obtained in (1). A little rearrangement should then provide the proof in the required format.

Yeah sort of, well it just says about writing down a recurrence relation from a given sequence formula and prove that the recurrence relation matches that formula, I attached an image to the post so you can see it.


Okay well I'm not sure how to get to the formula they asked me to prove from where I got to now, as I got to a place where I got a formula for un+1

I don't know how they approached this in the solution bank, but what I would suggest is:

1) Start with the given expression for u_n and rearrange it to make (2/3)^n the subject.

2) Move on to the expression for u_(n+1), based on the expression for u_n. Substitute in the expression for (2/3)^n you obtained in (1). A little rearrangement should then provide the proof in the required format.

Hi, I'm currently doing this question and don't understand step 2. Do you mind explaining?

Hi, I'm currently doing this question and don't understand step 2. Do you mind explaining?