Find nth term expression for following sequences...

the second one...

all the terms are even.... so what happens if you divide each one by 2 ?

1) 1/3, 2/5, 3/7, 4/9, 5/11

2) 2, 8, 18, 32, 50

3) 0, 1, 8, 27, 64

Can you show working out for each I don't know how to approach these types of questions.

Not going to give you answers, but even the answer to the first one seems a bit daft.

1. Look at the numbers themselves rather than the fractions. Comparing the numerators and the denominators each as a seperate sequence can give an answer.

2. As the bear said, divide them all by 2 and try and spot a pattern in the remaining numbers.

3. Cant really give any hints for this without giving it away. The sequence starts at n = 0 however.

But how would I arrange it into an expression once I figured out the pattern?

If you have the first term of something (where n=1), consider what you'd do to 1 to make it into the first number of the sequence. Then consider the 2nd term and the 3rd term etc. When you find that pattern, you have the nth term. This would be what would do to any number (n) to give the result in the nth position of the sequence.

I know that, but it's tricky to figure out what you would do to 1 to make it into the first number of the sequence when considering the other terms. I use the arithmetic sequence for Q1 for the denominator. But if I can't look for an arithmetic sequence what other methods are there other than dividing by 2? Could I possibly try to do simultaneous?

For the first, one, as an example, look at the numerators:

1, 2, 3, 4, 5

Then try and find the nth term of this sequence.

Then, look at the denominators:

3, 5, 7, 9, 11

Then try and find the nth term of this sequence.

And because we're dividing them, divide the nth term of the denominators by the nth term of the numerators.

I'm talking about the other 2 Q's I did Q1

Sorry, what did you get out of interest?

For question 2, after you divide by two, you get this sequence:

1, 4, 9, 16, 25

Then consider, what can you do with 1 (as in, the first term) to get an answer of 1? What about 2 (the second term) to get an answer of 4? And so on.

I got Un = 2/(2n-1) for Q1

For Q2 I tried when n=1, 2, 3, 4, 5 I could square n to get 1, 4,9,16,25

then times by 2 to go back to the normal sequence. Therefore Un = 2n^2.

Which is correct, thanks!

Well done, the first one is not quite right (I think you've wrote it in wrong).

Why divide the terms by 2 if they're even?