Deriving/Applying the Geometric Series Formula
Algebra · Flashcards · Recall
ALGEBRA · FLASHCARDS
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QUESTION
State the finite geometric series sum formula for
r
≠
1
r \neq 1
r
=
1
using
a
1
a_1
a
1
,
r
r
r
, and
n
n
n
(alternate form).
QUESTION
What is
S
n
−
r
S
n
S_n-rS_n
S
n
−
r
S
n
for a geometric series with first term
a
1
a_1
a
1
and ratio
r
r
r
?
QUESTION
What is the first term
a
1
a_1
a
1
in terms of
a
n
a_n
a
n
,
r
r
r
, and
n
n
n
for a geometric sequence?
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ANSWER
a
1
=
a
n
r
n
−
1
a_1=\frac{a_n}{r^{n-1}}
a
1
=
r
n
−
1
a
n
. Solve
a
n
=
a
1
r
n
−
1
a_n=a_1r^{n-1}
a
n
=
a
1
r
n
−
1
for
a
1
a_1
a
1
by dividing by
r
n
−
1
r^{n-1}
r
n
−
1
.
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