GEOMETRIC SEQUENCE FORMULAS Machinery's Handbook, 31st Edition
41
Geometric Sequence Formulas
To Find
Given
Use Formula
l r n – 1 = ------
l
n r
a
r – 1 ( ) S r n – 1 = ----------
n r
S
a
a
l
r
S
a lr r – 1 ( ) S = –
l
n S
a S a – ( ) n – 1
l S l – ( ) n – 1 =
ar n – 1 =
a n r
l
1 r -- a r – 1 ( ) S + [ ] =
a r
S
l
l
a n S
l S l – ( ) n – 1
a S a – ( ) n – 1 =
S r – 1 ( ) r n – 1 r n – 1 = ---------------- r log = -------------- + 1 l log a – log
n r
S
l
a l
r
n
a r – 1 ( ) S + [ ] log r log = ------------------------------ a – log S a – ( ) log S l – ( ) – log = ---------------------------- + 1 l log a – log l log lr r – 1 ( ) S – [ ] – log r log = ------------------------------ + 1
a r
S
n
n
a l
S
n
l
r
S
n
l n -- n – 1 =
a l
n
r
Sr a --- a S – a = + ------
a n S
r n
r
S a – S l – = ------
a l
S
r
Sr n – 1 S l – --------
l S l – – -----
l
n S
r n
=
a r n – 1 ( ) r – 1 = -----------
a n r
S
lr a – r – 1 = -------
a l
r
S
S
l n n – 1
n – 1 –
a n
a l
n
l n – 1 – = -------------------- n – 1 a
S
l r n – 1 ( ) r – 1 ( ) r n – 1 = --------------
l
n r
S
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