Hello guys, I need help solving the following question:
The sum of the first three terms in a geometric progression is 195. The difference (?) between the first and second term is larger in 75 than the third term. Find the first term and the common ratio of the given progression.
I a1 + a2 + a3 = 195
II a2 - a1 = a3 + 75
Could I please have the full solution? (because I reached a stage where I couldn't continue and didn't know what to do next)
Thanks in advance.
Thanks a lot for your help. No there's no typo, the r is supposed to have two solutions: 1/3 and -4/3. But the problem is that the discriminant of the quadratic equation is negative!
Where's my mistake? I can't find it!
There's no mistake. Topsquark has already implied this technical infelicity:
Originally Posted by loui1410
which is why he asked if there's a typo.
Originally Posted by topsquark
If there's no typo in what you posted, then the typo must be in the source of the question (textbook? problem sheet from class? Such things aren't infallible ......)
Alternatively, Topsquark's (quite reasonable) mathematical interpretation of
"The difference (?) between the first and second term is larger in 75 than the third term."
could be different to what the source of the question intends .....
It is supposed to be , not as I thought. The language which was the question originally written in is not my mother-tongue, and English isn't my mother-tongue neither. So sorry guys, it was only a result of mistranslation :p Anyway, I reached the correct solution now.