Geometric Sequences

Hi, I'm unsure about something...

In these examples, you'll notice that one of the questions has first term multiplied by common ratio to the power of n-1. So they can find out what n is. However, in the other example, they have a multiplied by the common ratio to the power of n... why are they not using to the power of n-1 and just using n? When do you determine when to use n-1 or just n.

https://gyazo.com/817a5a40fd85a6086b5e8bdb4f7e53f8

https://gyazo.com/09f87c7e9565f8c1711e26e04294c31d

Reply 1

constellarknight

2

In the first question, we simply care about the term number, so use (n-1) from the GP nth term formula.
In the second question, we want a number of years: the end of the 1st year is the 2nd term etc. so we use n.

Reply 2

Naruke

OP

11

Original post by constellarknight

In the first question, we simply care about the term number, so use (n-1) from the GP nth term formula.
In the second question, we want a number of years: the end of the 1st year is the 2nd term etc. so we use n.

I don't understand unfortunately.

To me they both look like normal geometric progressions, so why can't I use n - 1

:s-smilie:

Reply 3

Excuse Me!

19

Original post by Naruke

Hi, I'm unsure about something...

In these examples, you'll notice that one of the questions has first term multiplied by common ratio to the power of n-1. So they can find out what n is. However, in the other example, they have a multiplied by the common ratio to the power of n... why are they not using to the power of n-1 and just using n? When do you determine when to use n-1 or just n.

https://gyazo.com/817a5a40fd85a6086b5e8bdb4f7e53f8

https://gyazo.com/09f87c7e9565f8c1711e26e04294c31d

x_n = ar^(n-1)

Q1

a= 3 (it tells you the first term)
r= 4 (shown)
n = unkown (therefore we will use (n-1)

If the term exceeds 1 000 000, than it is greater than 1 000 000 so we use the > symbol to show term we need to find is greater than 1 000 000

a x r^{(n-1) >}1 000 000
3 x 4^{(n-1) >}1 000 000

Now solve with logs

4^{(n-1) >}1 000 000 / 3 etc.

Q2

They've said the first term is £A and have told us the multiplication factor is 0.85.

a = A
r = 0.85

We are working given the price after 3 years. The sequence will look like this

Original price, price after year 1, price after year 2, price after year 3, price after year 4 etc.

We know the price after 3 years. So if we look at the sequence the price after 3 years is given by term 4. Therefore:

n = 4

Put the information into our formula:

a x r^(n-1) = 11 054.25
a x (0.85)^(4-1)= 11 054.25
a x (0.85)⁽³⁾= 11 054.25

Then you'll go into solve the formula again.

So you don't use (n-1) in the second question because you know the value of n and are trying to work out a. You use (n-1) in the first question because you are trying to work out what n is and do not know what it is already!

Geometric Sequences

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