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August 31st, 2016, 07:09 AM  #1 
Newbie Joined: Aug 2016 From: Bucharest Posts: 14 Thanks: 0  Geometric Progression
In a geometric progression , (an)n>=1 , we know Sn=5^n*4 . Find b8 . I know the Sn formula but I don't know how to relate to it . Thank you ! 
August 31st, 2016, 07:23 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,640 Thanks: 2624 Math Focus: Mainly analysis and algebra 
What is "b8"? Do you mean $a_8$?

August 31st, 2016, 07:32 AM  #3 
Newbie Joined: Aug 2016 From: Bucharest Posts: 14 Thanks: 0  
August 31st, 2016, 12:56 PM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,887 Thanks: 1506  Quote:
Quote:
assuming $S_n = 5^n \cdot 4$ ... $S_7 + a_8 = S_8 \implies S_8  S_7 = a_8 = 5^8 \cdot 4  5^7 \cdot 4 = 5^7 \cdot 4 (5  1) = 5^7 \cdot 4^2$  
August 31st, 2016, 11:23 PM  #5 
Newbie Joined: Aug 2016 From: Bucharest Posts: 14 Thanks: 0  
September 1st, 2016, 09:11 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,484 Thanks: 2041 
The problem doesn't make sense. The formula $S_n = 5^n \cdot 4$ implies $a_1$ = 20, $a_2$ = 80, $a_3$ = 400, etc., which isn't a geometric progression, as 80/20 = 4, whereas 400/80 = 5. 

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