# Nth Term question

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

What is the nth term of

3, 3root5, 15, 15root5, 75

What is the nth term of

3, 3root5, 15, 15root5, 75

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#2

(Original post by

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

What is the nth term of

3, 3root5, 15, 15root5, 75

**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

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(Original post by

Youve been taught two types of sequences. Which is it?

**mqb2766**)Youve been taught two types of sequences. Which is it?

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?

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#5

(Original post by

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?

**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?

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#6

**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

3 * sqrt5 = 3sqrt5

3 sqrt5 * sqrt5 = 3 * 5 = 15

15 * sqrt5 = 15 sqrt5

15 * sqrt5 * sqrt5 = 15 * 5 = 75

Work from there

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(Original post by

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

**-Imperator-**)What number do you multiply each of those terms by to get the next?

1 = root 9

2 = root 45

3 = root 225

4 = root 1124

5 = root 5625

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#8

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

Spoiler:

Show

3 * sqrt5^(n-1)

Three times square root 3 to the power of n minus one

This is because each term is the previous term multiplied by square root 5

So,

3

3*(sqrt5)^1

3*(sqrt5)^2

3*(sqrt5)^3

Each term is 3*sqrt5 with the power increasing by one every time. The power is one below the term number

Therefore 3 * sqrt5^(n-1)

Three times square root 3 to the power of n minus one

This is because each term is the previous term multiplied by square root 5

So,

3

3*(sqrt5)^1

3*(sqrt5)^2

3*(sqrt5)^3

Each term is 3*sqrt5 with the power increasing by one every time. The power is one below the term number

Therefore 3 * sqrt5^(n-1)

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(Original post by

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?

**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?

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#10

(Original post by

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?

**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?

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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.

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(Original post by

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

**OJlongley**)If you're still stuck then here's the answer

Spoiler:

Show

3 * sqrt5^(n-1)

Three times square root 3 to the power of n minus one

This is because each term is the previous term multiplied by square root 5

So,

3

3*(sqrt5)^1

3*(sqrt5)^2

3*(sqrt5)^3

Each term is 3*sqrt5 with the power increasing by one every time. The power is one below the term number

Therefore 3 * sqrt5^(n-1)

Three times square root 3 to the power of n minus one

This is because each term is the previous term multiplied by square root 5

So,

3

3*(sqrt5)^1

3*(sqrt5)^2

3*(sqrt5)^3

Each term is 3*sqrt5 with the power increasing by one every time. The power is one below the term number

Therefore 3 * sqrt5^(n-1)

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#13

(Original post by

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.

**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.

* 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/s...es-series.html

Last edited by mqb2766; 1 month ago

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(Original post by

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/s...es-series.html

**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/s...es-series.html

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#15

(Original post by

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.

**14bearmanl**)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.

sqrt(5) ~ 2

and do approximate differences. However, its fairly clear that the differences increase faster than linear and successive ratios gives a constant r=sqrt(5).

Last edited by mqb2766; 1 month ago

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#16

(Original post by

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

**14bearmanl**)Thanks - I def need to practice these more. Thanks so much.

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