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NOTES ON ALGEBRA. 69
In the above example of a descending series :
a = 20-, /=8; d=2; n = 7; j = 98.
Formulas
:
Examples
:
a = l+(n — l)X d a = 8 + (7 — 1) X 2 = 20
l=a — (n — 1) X ^ /=20 — (7 — 1) X 2 = 8
;/ — 1 7 — 1
n = a ~ l
+ 1 « = 20 ~ 8
+1 = 7
, = *±I X.
. * = »±? X 7 = 9S
GEOMETRICAL PROGRESSION.
A Geometrical Progression is a series of numbers which
increase or decrease by a common constant ratio. For
instance :
3, 6, 12, 24, 48, is an ascending series ; 48, 24, 12, 6, 3 is a
descending series.
The following are the elements considered in a geometrical
progression
:
a = first term : / = last term : r = ratio ; n = number
of term ; s = sum of the terms.
When three of these are known the other two may be cal-
culated.
In this example of an ascending series :
a = 3 ; / = 48 ; r = 2 ; n = b; s = 93.
Formulas
:
Examples :
- _ ’I -— 48 _ 48 _ 48 _ g
,-n-i 2 s-1 24
16
/= a X r"’ 1
/=3X2 Sr~1 = 3 X 16 = 48
V4 -#= -’-
5-1 4
3
„ = /^.48-/^.3
+ 1 =
_ log. I -log, a ,
j %• 2
7^ 1.681241-0.477121 _ 5
0.30103
^ = /_X^__^ j = 48 X2-3 ^ 93
r—
1
2—1
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