Good evening, I've been struggling with this one for a while now.
The sum of an increasing geometrical progression is equal to 65. If we substract 1 from the smallest number there, and 19 from the biggest, the three numbers are going to form an arithmetical progression. Find these numbers.
I've gone trough many methods and none of them worked, so I't would be nice if you could explain this step by step. Not to look like someone just hunting for answers, I'll provide what I know:
The geometric progression, consisted of members b1, b2, b3. The sum of it is equal to 65. b1q = b2; b1q^2=b3
The aritmetic progression, consisted of a1, a2, a3. a1 = b1 - 1; a2 = b2 ; a3 = b3 - 19. a1 + d = a2, a1 + 2d = a3 I'm sort of new to this site, so sorry if I didnt provide something, like tags, because these type of things are called progressions here and there no such things in tag list. Im in 12th grade which is equal to senior year in USA as far as I know if that matters. thank you!