Page 9 - (1-1)eng

Elly fat mn 3omry ( 1 – 1 )
Exponents

+
If a   – { 1 }, then
0
 a = 1

 a  n  1
a n
m
n
m
n
 a = a
m
n
 a  a = a m + n
a m
= a m – n
a n
n
  a m   a m n

Arithmetic Sequence

 ( T n ) = ( a , a + d , a + 2 d , a + 3 d , . . . )
 T n = a + ( n – 1 ) d

 ( a, b, c ) is an A.S.  a + c = 2 b

n

 S n = [ 2 a + ( n – 1 ) d ]
2

= n a  
2
where a is the first term,  is the last term, d is the common difference and n is the number of terms

Geometric Sequence

2
3
 ( T n ) = ( a , a r , a r , a r , . . . )
 T n = a r n – 1
2
 ( a, b , c ) is a G.S.  b = a c

 a r n 1 
 S n = , r ≠ 1
r 1

=  r a , r ≠ 1

r 1
 S ∞ = a , | r | < 1
1  r
where a is the first term,  is the last term, r is the common ratio and n is the number of terms

Calculus 8 Unit (1)