Series and Sequences HSC question (1 Viewer)

[BlueGas]

I need help with this question, and also please explain how you came up with your working out because this is a tricky question, thanks alot!

 

[VBN2470]

I need help with this question, and also please explain how you came up with your working out because this is a tricky question, thanks alot!

To start you off with (b) (i),



Let me break it down for you:

- In the beginning of the first month, he deposit $500
- At the end of the month he will have an accumulated value of 500(1.003)
- At the start of the 2nd month, he will deposited 1% more than the previous deposit, which is 500(1.01)
- At the end of the 2nd month, the total balance in his account i.e. 500(1.003)+500(1.01) will have accumulated to (500(1.003)+500(1.01))*(1.003) which gives the desired result

For (b) (ii), try to continue the process as above and identify any patterns that may be relevant.

 

[BlueGas]

To start you off with (b) (i),



Let me break it down for you:

- In the beginning of the first month, he deposit $500
- At the end of the month he will have an accumulated value of 500(1.003)
- At the start of the 2nd month, he will deposited 1% more than the previous deposit, which is 500(1.01)
- At the end of the 2nd month, the total balance in his account i.e. 500(1.003)+500(1.01) will have accumulated to (500(1.003)+500(1.01))*(1.003) which gives the desired result

For (b) (ii), try to continue the process as above and identify any patterns that may be relevant.

Thanks man, makes much more sense now.

 

[BlueGas]

To start you off with (b) (i),



Let me break it down for you:

- In the beginning of the first month, he deposit $500
- At the end of the month he will have an accumulated value of 500(1.003)
- At the start of the 2nd month, he will deposited 1% more than the previous deposit, which is 500(1.01)
- At the end of the 2nd month, the total balance in his account i.e. 500(1.003)+500(1.01) will have accumulated to (500(1.003)+500(1.01))*(1.003) which gives the desired result

For (b) (ii), try to continue the process as above and identify any patterns that may be relevant.

If you don't mind can you explain how you get the total balance of the 3rd month?

 

[VBN2470]

If you don't mind can you explain how you get the total balance of the 3rd month?

- At the start of the 3rd month, he will have deposited 1% more than the previous deposit, which is now 500(1.01)*(1.01)
- Therefore, at the end of the 3rd month the total balance in his account, which is now will have accumulated to which you can simplify further.

Keep repeating this process for future months and you will start to see a pattern, so that you can get a generalised formula for the total balance at the end of the th month.

 

[BlueGas]

- At the start of the 3rd month, he will have deposited 1% more than the previous deposit, which is now 500(1.01)*(1.01)
- Therefore, at the end of the 3rd month the total balance in his account, which is now will have accumulated to which you can simplify further.

Keep repeating this process for future months and you will start to see a pattern, so that you can get a generalised formula for the total balance at the end of the th month.

Why can't you multiply the total balance of the 2nd month by (1.01) to get the start of the 3rd month, and then to get the end of the 3rd month, you multiply what you got by (1.003)?

 

[VBN2470]

The 1.01 factor refers to how much he deposits every month into the bank account, whereas the 1.003 refers to the total accumulated value of the balance at the end of the month. So, AFTER he deposits the monthly amount, THEN whatever the value of the account, it will be multiplied by 1.003 (interest) to get the total accumulated value at the end of the month.