Question

Ciąg arytmetyczny

zadania w załączniku

Answer 1

1

a9 = - 53

a22= -92

 

z właściwości ciągu arytmetycznego

 

a9 = a1+8r

a22 = a1+21r

 

a1+8r = -53

a1+21r = -92

 

-13r = 39

r = -3 to nasza różnica

 

a1+8*-3 = -53

a1-24 = -53

a1 = -29

 

 

b)

a7 = 47

a13 = 89

 

a7 = a1+6r

a13 = a1+12r

 

a1+6r = 47

a1+12r =89

 

-6r = -42

r = 7

 

a1+6*7 = 47

a1 = 47-42 =5

 

c)

a11 = 5

a21 = 0

 

a1+10r=5

a1+20r = 0

 

-10r = 5

r = -5/10 = -1/2

 

a1+10*-1/2 = 5

a1= 10

 

2

a6 = 13

a10 = 25

 

a1+5r =13

a1+9r =25

 

-4r = -12

r =3

 

a1+5*3 =13

a1 = -2

 

a15 = a1+14r = -2+14*3 = -2+42 = 40

 

3

a1 = k+1

a2 = 4k+1

a3 = 10k+7

 

z własciwości ciągu atrm.

 

a2-a1 = a3-a2

4k+1 -k-1 = 10k+7 -4k-1

3k-6k = 6

-3k = 6

k= -2

 

nasze wyrazy ciągu 

a1= k+1 = -2+1 = -1

a2 = 4k+1 = -8+1 = -7

a3 = 10k+7 = -20+7 = -13