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August 31st, 2016, 07:09 AM   #1
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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 !
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August 31st, 2016, 07:23 AM   #2
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What is "b8"? Do you mean $a_8$?
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August 31st, 2016, 07:32 AM   #3
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What is "b8"? Do you mean $a_8$?
Yes I solve arithmetic ones with a terms and geometric with b terms .
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August 31st, 2016, 12:56 PM   #4
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Originally Posted by MxMMxM View Post
Yes I solve arithmetic ones with a terms and geometric with b terms .
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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 $S_n = 5^n \cdot 4$ ...

$S_7 + a_8 = S_8 \implies S_8 - S_7 = a_8 = 5^8 \cdot 4 - 5^7 \cdot 4 = 5^7 \cdot 4 (5 - 1) = 5^7 \cdot 4^2$
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August 31st, 2016, 11:23 PM   #5
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Quote:
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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 !
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September 1st, 2016, 09:11 PM   #6
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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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