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Flashcards in Algebra Deck (12)
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1

equivalent transformation of inequality: x> y + a

x + a > y +a

2

important inequality with absolute values

|X + Y| <= |X| + |Y|

3

sequence

a list of objects separated by comma

4

arithmetic sequence (what is it)

An=A1 + d(n-1); d - common difference = An-An-1

5

the same of the first n terms of an arithmetic sequence

Sn=(A1+An)/2 X n or Sn=(2A1+d(n-1))/2 X n

6

geometric sequence

the riot between any two consecutive terms is the same.
An/An-1 = Q; An=An-1 X Q

7

geometric sequence of nth term

An=A1 X Q^(n-1)

8

sometimes a problem will provide two inequalities and ask you to combine them in some way

How to solve:
2 < X < 5; 3
find max and min:
5-3=2 (max)
2-3=-1
2-10= -8 (min)
5-10= -5
Finally: -8

9

absolute values: if a >0

|X|=a -> X = a or X= -a.

10

absolute values: if |X| < a

-a -3 0

11

absolute values: if |X| > a

or X>A or X |X-3| > 3 -> X-3>3 or X-3 or X>6 or X<0

12

Sqroot of X^2?

|X|