Ahad, 11 Januari 2009

Chapter 1 Progression

Arimethic Progression

a , a + d , a + 2d , a + 3d , ……..

a = first term
d = common terms

Formula

Tn = a (n-1)d

Sn = n/2 [ 2a(n-1)d ]

Geometric Progression

a , ar , ar^2 , ar^3 , …….

Formula

Tn = a(r^n-1)/(r-1) , when r > 1

Tn = a(1-r^n)/(1-r) , when r < 1



S infinity = a / r-1






Example
1. The third and the eighth term of an arithmetic progression are 22 and 57 respectively. Find
the first term and the common difference.

Tn = a + (n-1) d
T3 = a + (3-1) d = 22
= a + 2d = 22
= a = 22 - 2d - eq 1

T8 = a + (8-1) d = 57
= a + 7d = 57 - eq 2

replace eq 1 into eq 2

(22 - 2d) + 7d = 57
5d = 35
d = 7

when d = 7
a = 22 - 2 (7)
a = 8






2. Calculate the sum of all the terms for each of the arithmetic progressions below.

2, 6, 10, 14, ...... 50
Tn = 50
a + (n-1) = 50
2 + (n-1)4 = 50
4n - 4 = 48
4n = 52
n = 13

Sn = n/2(a + l)
S13 = 13/2 (2 + 50)
= 338

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