Number Patterns Module Help

[Yacoubb]

Hey guys

Just wondering, sometimes when it asks to find a particular term, it says after 10 years. However, sometimes it means that n = 10, and other times it means n = 11. How do I know when to use either of them?

[MagicGecko]

Hey guys

Just wondering, sometimes when it asks to find a particular term, it says after 10 years. However, sometimes it means that n = 10, and other times it means n = 11. How do I know when to use either of them?

With questions like these you have to read them carefully, it actually depends in what its asking. If it asks find the rate (or whatever) AFTER 'n' years then it would be the 'n+1' years. For example: *after some background info* How many sheep will be born after 10 years?...you would obviously use 11 as it is after 10.

[Zealous]

Just expanding on what Horacio said:
I like to just write down next to the question if the term they are giving you is like the first term of the sequence or the initial term before the sequence starts.

For example, from a VCAA exam a question was:

"A crystal measured 12cm in length at the beginning of a chemistry experiment. Each day it increased in length by 3%, the length after 14 days of growth is?"

I write down that initally the length is 12cm before any days have past, so the equation will be:

Spoiler

Personally for this question, I wrote next to the question "after 1 day of growth, it will 12.36".

as you want the growth to happen 14 times (after 14 days), so in this case you don't use "n-1" as the 12cm is like the initial term before the first day of growth.


An example of the case in which you use "n-1" is:

"In the first month, the gardeners worked 625 hours. In the second month, the gardeners worked 500 hours. How many hours did they work in the fifth month.

Now we know the first term of the sequence is 625, so we have to use "n-1" or else we will generate a sequence after the first month. I wrote next to the wording there.

Hopefully that made some sense, I get so annoyed by the wording we get in some of the questions like "during", "after", "more". Or the questions when they want you to find how much "n" until one sequence reaches over a certain value.

[Yacoubb]

Just expanding on what Horacio said:
I like to just write down next to the question if the term they are giving you is like the first term of the sequence or the initial term before the sequence starts.

For example, from a VCAA exam a question was:

"A crystal measured 12cm in length at the beginning of a chemistry experiment. Each day it increased in length by 3%, the length after 14 days of growth is?"

I write down that initally the length is 12cm before any days have past, so the equation will be:

Spoiler

Personally for this question, I wrote next to the question "after 1 day of growth, it will 12.36".

as you want the growth to happen 14 times (after 14 days), so in this case you don't use "n-1" as the 12cm is like the initial term before the first day of growth.


An example of the case in which you use "n-1" is:

"In the first month, the gardeners worked 625 hours. In the second month, the gardeners worked 500 hours. How many hours did they work in the fifth month.

Now we know the first term of the sequence is 625, so we have to use "n-1" or else we will generate a sequence after the first month. I wrote next to the wording there.

Hopefully that made some sense, I get so annoyed by the wording we get in some of the questions like "during", "after", "more". Or the questions when they want you to find how much "n" until one sequence reaches over a certain value.

THANK YOU SO MUCH! This has been bugging me for a while, and I actually understand that now 100%. Straight to my bound reference, haha. Thanks so much!