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# Geometric Progression watch

1. The sum of the 1st and 2nd terms of a geometric progression is 50 and the sum of the 2nd and 3rd terms is 30. Find the sum to infinity.
2. (Original post by Multifine)
The sum of the 1st and 2nd terms of a geometric progression is 50 and the sum of the 2nd and 3rd terms is 30. Find the sum to infinity.
What have you tried?
3. (Original post by SeanFM;[url="tel:69964212")
69964212[/url]]What have you tried?
Well I used the formula for the sum of succeeding terms in a geometric progression, Sn = a(1-r^n)/1-r, substituting and getting two simultaneous equations:

a(1-r^2)/1-r = 50 ------------1

a(1-r^3)/1-r = 30 + a --------------2

Now I keep getting stuck every time I attempt to substitute a variable into another . . .

Once I can find out either a or r, I can do the rest.
4. (Original post by Multifine)
Well I used the formula for the sum of succeeding terms in a geometric progression, Sn = a(1-r^n)/1-r, substituting and getting two simultaneous equations:

a(1-r^2)/1-r = 50 ------------1

a(1-r^3)/1-r = 30 + a --------------2

Now I keep getting stuck every time I attempt to substitute a variable into another . . .

Once I can find out either a or r, I can do the rest.
That is tricky yes, I'd suggest going back and down another route.

You have that a+ar = 50 and ar + ar^2 = 30. The latter is equivalent to r(a+ar) = 30.

Does this help?
5. (Original post by SeanFM;[url="tel:69964584")
69964584[/url]]That is tricky yes, I'd suggest going back and down another route.

You have that a+ar = 50 and ar + ar^2 = 30. The latter is equivalent to r(a+ar) = 30.

Does this help?
Mm yes it does, I haven’t thought of that. Thank you, but I’m quite worried that if I had such a question in my paper, and if I wouldn’t have thought this way, I wouldn’t be able to solve it.
6. Thread moved to maths. Multifine Please post in the maths forum for maths subject questions, thanks
7. (Original post by Multifine)
Mm yes it does, I haven’t thought of that. Thank you, but I’m quite worried that if I had such a question in my paper, and if I wouldn’t have thought this way, I wouldn’t be able to solve it.
that is why it is important to do lots of different questions before the exams.

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Updated: February 6, 2017
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