Question

Wypisz pięć początkowych wyrazów ciągu, jeżeli ciąg jest określony wzorem

Answer 1

a) an = n² - 3n

b) an = (2n+2)/3n

c) an = (2n + (-1)^n)/3n

 

Po prostu podstawiamy za n, który wyraz chcemy wyliczyć, np jeśli chcemy pierwszy, to:

 

a)

 

a1 = 1 - 3 = -2

a2 = 4 - 6 = -2

a3 = 9 - 9 = 0

a4 = 16 - 12 = 4

a5 = 25 - 15 = 10

 

b)

 

a1 = 2+2/3 = 4/3

a2 = 4+2/6 = 1

a3 = 6+2/9=8/9

a4 = 8+2/12=10/12

a5 = 10+2/15 = 12/15 = 4/5

 

c)

 

a1 = 2-1/3 = 1/3

a2 = 4+1/6 = 5/6

a3 = 6-1/9 = 5/9

a4 = 8+1/12=9/12=3/4

a5 = 10-1/15=9/15=3/5

Answer 2

a)

a1= 1-3= -2

a2= 4-6= -2

a3= 9-9= 0

a4= 16-12=4

a5= 25=15=10

 

b) a1= (2+2)/3= 4/3=   1 i 1/3

a2= (4+2)/6=1

a3=(6+2)/8=1

a4=( 8+2)/12= 5/6

a5= (10+2)/15= 4/5

 

c)a1= (2-1)/3=1/3

a2= (4+1/6)= 5/6

a3= (6-1)/9= 5/9

a4= (8+1)/12= 3/4

a5= (10-1)/15= 3/5