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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

In a GP, u3 = 18 and u5 = 162. Find u1.

I know that in a GP, ux / u(x-1) = ratio (r). I deduce from that;

u5 / n == n / u3.

so 162 / n = n / 18

I then try to balance this - I think that's where I am going wrong.

162 = 2n/18

2916 = 36n

n = 81

Which is of course incorrect. Where am I going wrong?

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

162 = n² / 18n

Is this along the right track?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,012

*In a GP, u3 = 18 and u5 = 162. Find u1.*

rickyoswaldiow,

u3*n=u4, u3*n²=u5

That is, n²=u5/u3=162/18=9, n=3.

u1*n²=u3. Therefore, u1*9=18, u1=2.

The Geometric Progression is 2, 6, 18, 54, 162, 486.....

The first term is 2 and the common ratio is 3.

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

Thanks Ganesh. Will have to study this a bit more

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

ux / u(x-1) = ratio

Is this correct?

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**Ikcelaks****Member**- Registered: 2006-03-13
- Posts: 8

You setup the equation right, but your algebra is incorrect.

162 / n = n / 18

162 = n^2 / 18 (this is where you went wrong)

162 * 18 = n^2

2916 = n^2

54 = n

You should be able to work out the rest for yourself.

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