iheartfood
In a geometric sequence, the term an+1 can be smaller than the term an.
true or false?
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irkiz
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true
irkiz
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if n is < 1
iheartfood
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are u sure?? how did u know so fast?? lol
irkiz
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as in |n| < 1
irkiz
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so n ranges from 0 to 1
irkiz
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oops
irkiz
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wait
iheartfood
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oh okay
irkiz
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if the interval is (-1) that makes it alternating
irkiz
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so it will be smaller and bigger alternatingly
irkiz
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(-1)^ 2 is positive, (-2) ^ 3 is negative
iheartfood
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so this is FALSE?
irkiz
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(-2)^2 i mean
campbell_st
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if the common ratio r <1 then each term is smaller that the previous
irkiz
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there are a few cases yeah.
if the sequence convergerges or if the sign alternates
iheartfood
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wait so its TRUE then???
irkiz
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yup its true
irkiz
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i said wait coz my explanation was incomplete
iheartfood
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oh okay haha :P thanks!!! so its definitely TRUE right?
campbell_st
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if the absolute value of r is less than 1 |r| < 1 the the geometric series will have a limiting sum...
campbell_st
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just to clarify things... n is used for the term number... and r is used for the common ratio ( or multiplication constant)...
just to avoid confusion.
iheartfood
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k thanks for all the help y'all!
irkiz
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yeah.
\[ar ^{n}\]
if |r| < 1 it converges and if r is negative, it alternates
campbell_st
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not quite a term in a geometric series is found using
\[T_{n} = ar^{n -1}\]
n is the term number, T is the Term a is the 1st term and r is the common ratio...
please get it right @irkiz
iheartfood
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k thanks for all the help y'all!