Nth Term question

Original post by 14bearmanl

Because it's a root - it looks like a quadratic sequence - each time increasing by a multiple of root5. Not sure what to do next?

3 (times root5) = 3 root 5, or is it 3 to the power of n times root 5 - getting really confused. What do I do next?

For a quadratic sequence, when you difference successive terms that forms a linear or arithmetic sequence. Does that happen here? If not, what else could it be?

Reply 5

OJlongley

12

Original post by 14bearmanl

I've been staring at this GCSE question all day - can anyone help?

What is the nth term of

3, 3root5, 15, 15root5, 75

The change between each number is root 5
3 * sqrt5 = 3sqrt5
3 sqrt5 * sqrt5 = 3 * 5 = 15
15 * sqrt5 = 15 sqrt5
15 * sqrt5 * sqrt5 = 15 * 5 = 75
Work from there

Reply 6

OP

Original post by -Imperator-

What number do you multiply each of those terms by to get the next?

Multiple by root 5? I tried turning them all into roots - and can see they are multiples of 5 - just don't know what to do next?

1 = root 9
2 = root 45
3 = root 225
4 = root 1124
5 = root 5625

Reply 7

OJlongley

12

If you're still stuck then here's the answer

Spoiler

Reply 8

OP

Original post by mqb2766

For a quadratic sequence, when you difference successive terms that forms a linear or arithmetic sequence. Does that happen here? If not, what else could it be?

Ah so it is a geometric progression sequence using surds, because it is increasing by root 5 each time. I'm still not sure how to work out the nth term on this?

Reply 9

Original post by 14bearmanl

Ah so it is a geometric progression sequence using surds, because it is increasing by root 5 each time. I'm still not sure how to work out the nth term on this?

What do you need to know for a geometric sequence nth term?

Reply 10

OP

Do I need to apply the formula for geometric sequence - I'd forgotten about this one. Am guessing I need to put the root 5 into the formula to get the nth term. Need to find some practice questions now. Thanks so much.

Reply 11

OP

Original post by OJlongley

If you're still stuck then here's the answer

Spoiler

Thanks - I def need to practice these more. Thanks so much.

Reply 12

Original post by 14bearmanl

Do I need to apply the formula for geometric sequence - I'd forgotten about this one. Am guessing I need to put the root 5 into the formula to get the nth term. Need to find some practice questions now. Thanks so much.

As a brief summary, you have arithmetic sequences (linear and quadratic) and geometric sequences. You can tell them apart by working out the difference and ratio of successive terms.
* If the difference is constant, its a linear arithmetic sequence
* If the difference increases linearly, its a quadratic sequence
* If the ratio is constant, its a geometric sequence.
When given a sequence, this is almost always the first thing to determine.

For each of these sequences, you need to know the initial term and the difference or ratio to get a formula for the nth term
https://www.mathsisfun.com/algebra/sequences-series.html

(edited 2 years ago)

Reply 13

OP

Original post by mqb2766

As a brief summary, you have arithmetic sequences (linear and quadratic) and geometric sequences. You can tell them apart by working out the difference and ratio of successive terms.
* If the difference is constant, its a linear arithmetic sequence
* If the difference increases linearly, its a quadratic sequence
* If the ratio is constant, its a geometric sequence.
When given a sequence, this is almost always the first thing to determine.

For each of these sequences, you need to know the initial term and the difference or ratio to get a formula for the nth term
https://www.mathsisfun.com/algebra/sequences-series.html

That's great - I'm going to take a look at this now. Just been doing so many quadratic sequences lately and looking at differences rather than ratios, I'd forgotten how to do it. Thanks so much.

Reply 14