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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: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra What is "b8"? Do you mean $a_8$?
August 31st, 2016, 07:32 AM   #3
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 Originally Posted by v8archie What is "b8"? Do you mean $a_8$?
Yes I solve arithmetic ones with a terms and geometric with b terms .

August 31st, 2016, 12:56 PM   #4
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 Originally Posted by MxMMxM Yes I solve arithmetic ones with a terms and geometric with b terms .
Quote:
 In a geometric progression , (an)n>=1 , we know Sn=5^n*4
note that the problem statement used $a_n$ to represent the nth term ...

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
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 Originally Posted by skeeter note that the problem statement used $a_n$ to represent the nth term ... assuming $S_n = 5^n \cdot 4$ ... $S_7 + a_8 = S_8 \implies S_8 - S_7 = a_8 = 5^8 \cdot 4 - 5^7 \cdot 4 = 5^7 \cdot 4 (5 - 1) = 5^7 \cdot 4^2$
Thank you very much !

 September 1st, 2016, 09:11 PM #6 Global Moderator   Joined: Dec 2006 Posts: 20,654 Thanks: 2087 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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