Urgent : Sg maths 2005 p1 q8

I have got the answer for this question but dont know how to get to it.

A number patter is is given below

1st term: 2² -0²
2nd Term:3²-1²
3rd term: 4²-2²

a) Write down a similar expression for the 4th term
b) Hence or otherwise find the nth term in its similar form.

a) is is easy and i hgotit in minutes but b is slightly confusing to me, the answer is 4n btw

Reply 1

mattypb

nth term: (n+1)^2 - (n-1)^2

expand and simplify

Reply 2

animelover123

OP

9

Original post by mattypb

nth term: (n+1)^2 - (n-1)^2

expand and simplify

i saw that in the solutions but done get it :frown:

Reply 3

Enzo-259

15

Original post by animelover123

i saw that in the solutions but done get it :frown:

Think of it like this:

What's actually happening each time in the pattern? The number on the left is one digit higher than the number of the term, and the number on the right is one lower.

i.e. for the 2nd term; number on left is 3 and number on right is 1.

Therefore if we sub it into the actual equation, you get

(3^2)-(1^2)

Now if we don't actually know what the term is, we can substitute the letter n (in other words, the nth term).

So it becomes

(n+1)^2-(n-1)^2

Which can be expanded to

(n+1)(n+1) - (n-1)(n-1)

And simplified to:

(n^2 + 2n + 1) - (n^2 - 2n + 1)

Which becomes:

4n

(edited 13 years ago)

Reply 4

animelover123

OP

9

Original post by Enzo-259

Think of it like this:

What's actually happening each time in the pattern? The number on the left is one digit higher than the number of the term, and the number on the right is one lower.

i.e. for the 2nd term; number on left is 3 and number on right is 1.

Therefore if we sub it into the actual equation, you get

(3^2)-(1^2)

Now if we don't actually know what the term is, we can substitute the letter n (in other words, the nth term).

So it becomes

(n+1)^2-(n-1)^2

Which can be expanded to

(n+1)(n+1) - (n-1)(n-1)

And simplified to:

(n^2 + 2n + 2) - (n^2 - 2n + 2)

Which becomes:

4n

Thanks that is more helpful than the last post. I understand it more :smile:

i didnt get why you need to add the =1 and -1 into the n's , but i get it now, youre gd at explaining stuff :biggrin:

Reply 5

Ecosse_14

19

Original post by Enzo-259

Think of it like this:

What's actually happening each time in the pattern? The number on the left is one digit higher than the number of the term, and the number on the right is one lower.

i.e. for the 2nd term; number on left is 3 and number on right is 1.

Therefore if we sub it into the actual equation, you get