ARITHMETIC SEQUENCE FORMULAS Arithmetic Sequence Formulas Machinery's Handbook, 31st Edition
40
To Find
Given
Use Formula
d l
n
n – 1 ( ) d = – n – 1 2 ------ d × = –
a l
S n -- d 2 --
d n S
a
a
1 2 -- 2 l d + ( ) 2 8 dS – ± =
d l
S
a
2 S n --- l = – l a – n – 1 = ------
l
n S
a
a l
n
d
2 S 2 an – n n – 1 ( ) = ----------- l 2 a 2 – 2 S l – a – = ------------ 2 nl 2 S – n n – 1 ( ) = -----------
a n S
d
d
a l
S
d
l
n S
d
a d n
a n – 1 ( ) d = +
l
1 2 -- 8 dS
d 2 –--
a d S
±
2 a d – ( ) 2 +
=
l
l
2 S n --- a = –
a n S
l
S n -- n – 1 2 ------ d × = +
d n S
l
1 l a – d = + -----
a d l
n
d 2 a – 2 d --------
1 2 d --- 8 dS
a d S
±
2 a d – ( ) 2 +
=
n
n
2 S a l + = ------
a l
S
n
2 l d + 2 d -------
1 2 d --- 2 l d + ( ) 2 8 dS – ±
d l
S
=
n
n 2 -- 2 a n – 1 ( ) d + [ ] =
a d n
S
l 2 a 2 – 2 d + --------
a l + 2 d ------ l d a + – ( )
a l + 2 ------
a d l
=
=
S
S
n ( a + l ) = 2
a l
n S n
n 2 -- 2 l n – 1 ( ) d – [ ] =
d l
n
S
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