You are Here: Home >< Maths

# Series and sequence Watch

1. The population of a colony of insects increases in such a way that if it is N at the beginning of the week, then at the end of the week it is a+bN, where a and b are constants and 0<b<1. Starting from the beginning of the week when the population is N, write down an expression for the population at the end of 2 weeks. Show that at the end of c consecutive weeks the population is a(1-bc/1-b)+bcN.

When a=2000 and b=0.2, it is known that the population takes about 4 weeks to increase from N to 2N. Estimate a value for N from this information.
2. (Original post by cucumberpj)
The population of a colony of insects increases in such a way that if it is N at the beginning of the week, then at the end of the week it is a+bN, where a and b are constants and 0<b<1. Starting from the beginning of the week when the population is N, write down an expression for the population at the end of 2 weeks. Show that at the end of c consecutive weeks the population is a(1-bc/1-b)+bcN.

When a=2000 and b=0.2, it is known that the population takes about 4 weeks to increase from N to 2N. Estimate a value for N from this information.
So how far have you got with this?
Can you show us some working?
3. (Original post by davros)
So how far have you got with this?
Can you show us some working?
I really don't know how to solve it...
I can't understand the question, it is A.P. or G.P.?
4. (Original post by cucumberpj)
I really don't know how to solve it...
I can't understand the question, it is A.P. or G.P.?
You have been given a formula

Start of W1 = N

End of W1 = a+bN

So start of W2 = a+bN

So what is end of W2
5. (Original post by TenOfThem)
You have been given a formula

Start of W1 = N

End of W1 = a+bN

So start of W2 = a+bN

So what is end of W2
End of W2 = a+bN+(a+bN-N)= 2a+2bN-N
Is it correct?
6. (Original post by cucumberpj)
End of W2 = a+bN+(a+bN-N)= 2a+2bN-N
Is it correct?
Where did you get that

The end of the week = a + b(start of week)
7. (Original post by cucumberpj)
I really don't know how to solve it...
I can't understand the question, it is A.P. or G.P.?
Forget about APs and GPs for the moment and just use the formula as TenOfThem suggests.

Whatever the start-value is at the beginning of the week, you are told that the end-value at the end of the week is given by the formula

end-value = a + b x start-value

So if you start the week with N, you end the week with a + bN.
So if you start the 2nd week with a + bN, what is the value at the end of the 2nd week?
8. (Original post by davros)
Forget about APs and GPs for the moment and just use the formula as TenOfThem suggests.

Whatever the start-value is at the beginning of the week, you are told that the end-value at the end of the week is given by the formula

end-value = a + b x start-value

So if you start the week with N, you end the week with a + bN.
So if you start the 2nd week with a + bN, what is the value at the end of the 2nd week?
a+b(a+bN)
i knew how to show it ,but now i don't know how to estimate a value for N.
9. (Original post by cucumberpj)
a+b(a+bN)
i knew how to show it ,but now i don't know how to estimate a value for N.
Have you done the bit about the result after c consecutive weeks?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 15, 2014
Today on TSR

Find out how.

### Want £10K to start a business?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.