Fichas
Sequence basics
Fichas del conjunto (10)
- 1How do we define the nth term of a sequence?un
- 2For the sequence 3,5,7,9 , what is u1 ,un and un+1u1 = 3
un = 2n+1
un+1 = un + 2 (as rule = +2) - 3If u1 = 10 , and un+1 = (5un -1)/10 , find u2, u3 and u4. (this is called an inductive definition)u2 = 5(10)-1 /10 = 4.9
u3 = 5(4.9)-1 /10 = 2.35
u4 = 5(2.35)-1 /10 = 1.075 - 4The sequence is an increasing sequence if....uk+1 > uk
- 5The sequence is a decreasing sequence if....uk+1 < uk
- 6The sequence is a periodic sequence if....The the pattern is repeated
- 7What is a converging sequence?A sequence that's nth term approaches a finite number as n becomes larger
- 8How do we find the limit of a converging sequence?We set un =L and un+1 = L (as un and un+1 must be equal) and rearrange for L.
- 9Find the limit of un+1 = (5un -1)/10L = 5L-1 /10 , 5L = -1 , L = -1/5
- 10For the equation x^10 - 3x^7 + 2x + 7 = 0 , find an expression for xn+1x^10 - 3x^7 + 2x + 7 = 0 ,
x^10 + 2x = 3x^7 - 7
x(x^9 + 2) = 3x^7 - 7 , x = (3x^7 -7) / (x^9 +2)
Therefore: xn+1 = (3xn^7 - 7) / (xn^9 + 2)