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Credit Maths Sequences trouble

Hello.

As you may know the exam starts soon, ive already started revising but in Credit maths ive got a problem with one topic:sequences. Ive done a few past papers and those questions trip me up the most. They are for a minor amount of marks, but i want to get it right.Here's an example:

1,3,5,7,

The first odd number can be expressed as 1=1²-0²
The second odd number can be expressed as 3=2²-1²
the third odd number can be expressed as 5=3²-2²

a. Express the 4th odd number in this form
b. Express the number 19 in this form
c. Write down a formula for the nth odd number and simplify this expression



thats the question, i hope someone can help me. the first 2 parts i get as they are easy , it the last part, anything about the nth term, i go clueless.

it would be appreciated if someone could tell me how to handle these questions, i dont want an answer as ive got it , i want to know how to handle these questions.

Thanks
Reply 1
Avatar for roar558
roar558
11
well let's go through this
the first odd number can be expressed as the number one squared- the number one less than one squared ie 0 squared
the second odd number can be expressed as the number two - the number one squared less than two squared ie 1 squared
if this continues the nth odd number can be expressed as the number n squared- the number one less than n squared ie n^2-(n-1)^2 which you can simplify

essentially look for the pattern in the terms they give you
(edited 13 years ago)
Reply 2
Avatar for animelover123
animelover123
OP
9
Original post by roar558
well let's go through this
the first odd number can be expressed as the number one squared- the number one less than one squared ie 0 squared
the second odd number can be expressed as the number two - the number one squared less than two squared ie 1 squared
if this continues the nth odd number can be expressed as the number n squared- the number one less than n squared ie n^2-(n-1)^2 which you can simplify

essentially look for the pattern in the terms they give you


I don't get that

Here ive got this:

1=1²-0²
3=2²-1
5=3²-2²
7=4²-3²

what next , how do i find the pattern?
Reply 3
Avatar for roar558
roar558
11
Original post by animelover123
I don't get that

Here ive got this:

1=1²-0²
3=2²-1
5=3²-2²
7=4²-3²

what next , how do i find the pattern?


the first term, let's call that N1=1^2-0^2
N2=2^2 - 1 ^2
N3=3^2 - 2^2
You should be able to tell by looking that what happens is that Nn=n^2 - (n-1)^2
Reply 4
Avatar for animelover123
animelover123
OP
9
Original post by roar558
the first term, let's call that N1=1^2-0^2
N2=2^2 - 1 ^2
N3=3^2 - 2^2
You should be able to tell by looking that what happens is that Nn=n^2 - (n-1)^2


Why minus 1?

Sorry I'm being a pain, but i really don't get this.

Never I'm i ge the minus 1 part now

I didn't know you could substitute the odd numbers on the left with the n thingy
(edited 13 years ago)
Reply 5
Avatar for roar558
roar558
11
Original post by animelover123
Why minus 1?

Sorry I'm being a pain, but i really don't get this.

Never I'm i ge the minus 1 part now

I didn't know you could substitute the odd numbers on the left with the n thingy


It's essentially what it's asking you to do when you're asked for the nth term, to write the equation in terms of n
Reply 6
Avatar for animelover123
animelover123
OP
9
Original post by roar558
It's essentially what it's asking you to do when you're asked for the nth term, to write the equation in terms of n


Thanks a lot for the help, and MAths meant to be one of my strongest subjects...Its these and indicies i cant do, everything else seem to be fine

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