Finding the common ratio of G.P.

Hello,

I am struggling with the following question: 'The third, fifth and seventeenth terms of an A.P. are in geometric progression. Find the common ratio of the G.P.

I have done the following:

Let the third, fifth and seventeenth terms be x, y and z respectively. From which I have, from A.P:

x + 2d = y

x + 14d = z

y + 12d = z

Also from G.P:

xr = y

xr^2 = z

yr = z

xz = y^2

I have three unknowns and seven equations, which I think should be enough, but I seem to be going round in circles. I would very much appreciate it if someone could point me in the right direction and/or suggest another approach.

Thank you.(Thinking)

Re: Finding the common ratio of G.P.

Let Leat AP have 1st term a and common difference d

Then we have (a+4d)/(a+2d)=(a+16d)/(a+4d)

Hence get a in terms of d and sub back in (a+4d)/(a+2d)

Re: Finding the common ratio of G.P.

Thank you.

I'll try that.

(Sun)

Re: Finding the common ratio of G.P.

Thank you again.

That worked, I got r = 6.

(Happy)

Re: Finding the common ratio of G.P.

could u pls show me how u arrive at 6 .

Re: Finding the common ratio of G.P.

Re: Finding the common ratio of G.P.

Re: Finding the common ratio of G.P.

i have 2 more problems

1. A geometric series has the first term 2 and common ratio 3/2

Find the greatest number of

terms the series can have without its sum exceeding 125.

2.. A geometric series has the first term 5 and common ratio 3. Find the least number of terms

the series can have if its sum exceeds 2000.

but for the first one i got 8.522 as the answer and 6.085 for the 2nd . but my tutor has a different answer 8 and 7 respectively and i donot know how she came about it could anyone show me .i think she must have approximated but i dont know what she has done precisely .

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