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OCR C2 Geometric Help!

In a geometric progression, the fifth term is 100 and the seventh term is 400. Find the first term.

Sorry I know this is easy! I was away when this topic was taught.

Reply 1

clownfan

Its not easy as you are unable to do it...

ok load up the the formula you would have to hand and see if you can deduce a simultaneous equation from it

Reply 2

Chrisjay17

ar^{n-1}

How do I deduce simultaneous eqns from this?

Reply 3

Goldfishy

For any term n in a GP:

n^{th} term = ar^{n-1}

Reply 4

Chrisjay17

I don't have any values for a and r though?

Reply 5

charlotte-rose

Chrisjay17

In a geometric progression, the fifth term is 100 and the seventh term is 400. Find the first term.

Sorry I know this is easy! I was away when this topic was taught.

Geometric progression - mulitiplied by a constant.
100*x = sixth term.

(100*x)*x=400
x^2=400/100
x^2=4
x= +2 or -2

100/2 = 50 (fourth) (positive or negative)
50/2 = 25 (third) (positive)
25/2 = 12.5 (second) (positive or negative)
12.5/2=6.25 (first) (positive)

Reply 6

Goldfishy

But do you need them? For the 5th term,

ar^4= 100

Do this for the 7th term to obtain the simultaneous equations, and then divide the larger by the smaller one.

EDIT: Or just give her the answer, either way...

Reply 7

clownfan

charlotte-rose

I don't like this post

Reply 8

charlotte-rose

clownfan

I don't like this post

Can I ask why?

Reply 9

charlotte-rose

Goldfishy

EDIT: Or just give her the answer, either way...

Gave her an explanation and then the answer, which I find is the best way to learn.

She's not going to get anywhere having to guess at As and Rs etc because it's clear she doesn't understand where you're coming from.

Reply 10

Physics Enemy

Chrisjay17

In a geometric progression, the fifth term is 100 and the seventh term is 400. Find the first term.

Sorry I know this is easy! I was away when this topic was taught.

Geometric Series: a, ar, ar^2, ar^3, ... ar^(n - 1)
5th term = 100 => ar^4 = 100
7th term = 400 => ar^6 = 400

The first term is a.

r^4 = 100/a, r^6 = 400/a. Also note: r^2 = 10/(Sqrta)

(100/a).10/(Sqrta) = 400/a
1000/(aSqrta) = 400/a
10/(Sqrta) = 4
Sqrta = 5/2

...

Reply 11

Goldfishy

charlotte-rose

Chrisjay17

ar^{n-1}

How do I deduce simultaneous eqns from this?

He* a and r are standard notation and as the OP clearly uses that notation I thought that was what he would be most familiar with. Also, I wouldn't really call your's an explanation as I don't have any clue what you did either. It would be more useful if the OP would try out the question with hints along the way instead of just a solution. So please don't slate my replies if your's are quite flawed.

Reply 12

hotshot45

cba to read other posts but i think you use the ar^n-1 formular for 5th and seventh term and then use simaltaneous equations...

Reply 13

charlotte-rose

Goldfishy

"or just give her the answer either way". I went on what you said, I didn't check for gender.

OP I apologise.

Geometric progession means terms are multiplied by constants.

Therefore term one * the constant = term 2
term 2 * the constant * the constant = term 4

it's a way of doing it without having to use simultaneous equations which some people dislike working with.

If someone gives me hints when I want to know how to do something I get quite annoyed, especially when my exam may be tomorrow morning. But how is my reply flawed? I went through it step by step, and came to an answer.

Reply 14

Goldfishy

charlotte-rose

Lol aren't I a bit of a hypocrite. I haven't actually done the question yet, but can sure say that I didn't understand any of what you wrote - sorry. I'm not too sure that the OP is bothered any more, but for what it's worth:

5th term:

ar^4 = 100

7th term:

ar^6 = 400

(7th term)/(5th term):

r^2 = 4

r= \pm 2

Subbing

\pm 2

into the 5th term:

a \times (\pm)2^4 = 100

16a =100

a = \frac {100}{16}

Reply 15

charlotte-rose

Goldfishy

ar^4 = 100

7th term:

ar^6 = 400

(7th term)/(5th term):

r^2 = 4

r= \pm 2

Subbing

\pm 2

into the 5th term:

a \times (\pm)2^4 = 100

32a =100

a = \frac {100}{32}

I understand what you've done, but it doesn't add up :s-smilie:

(using r=+2 to make it easier to read)

3.125*2 = 6.25 (second term)
6.25*2 = 12.5 (third term)
12.5*2 = 25 (fourth term)
25*2 = 50 (fifth term... but the fifth term was 100)

Reply 16

Goldfishy

charlotte-rose

I understand what you've done, but it doesn't add up :s-smilie:

(using r=+2 to make it easier to read)

3.125*2 = 6.25 (second term)
6.25*2 = 12.5 (third term)
12.5*2 = 25 (fourth term)
25*2 = 50 (fifth term... but the fifth term was 100)

My mistake, I put

2^4 = 32

for some reason :woo:

I've edited my original solution now.

Reply 17

clownfan

charlotte-rose

Can I ask why?

Sorry, I should have expanded on that..it looks a little blunt.

OK, I would not follow what you have written as you have not used the formula C2 students would use.

ar^(n-1) finds any term with a being the first, r being the ratio and n being the number of the term in the sequence.

In this problem we have

ar^4 = 100 (as the 5th term becomes 4)
ar^6 = 400 (as the 7th term becomes 6)

This is now clear and an 'easy' sim eq can be gained.

You have used a very general method which will not allow for the 234, 765th of 2879000226 term to be found for example and its not clear what to do in terms of the first term.

You have stated that a GP is multipled by a constant...So is an AP

So, in all it is (IMO) not an easy method to (a) follow) (b) assist learning (c) find higher terms.

I wasnt trying to be rude :smile: