Question

Zadanie 10

Answer 1

z.10

a)

a1 = 13

an+1 = 5 an  / : an

an+1 / an = 5   ---------------> q = 5

zatem

an = 13*5^(n -1)

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b1 = -0,4

bn+1 = bn / 7

zatem   bn+1 / bn = 1/7  ---> q = 1/7

czyli

bn =(-0,4)*(1/7) ^(n -1)

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c1 = 3/4

cn+1 = - 9 cn

zatem   cn+1 / cn =  - 9  ---> q = - 9

czyli

cn = (3/4)*(-9)^(n -1)

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b)

xn = 19*(-0,7)^(n -1)

czyli  x1 = 19   oraz q = - 0,7

xn+1 = 19*(-0,7) ^n

zatem xn+1 = -0,7 * xn

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yn = (-2/3)*(3/2)^n = (-2/3)*(3/2)*(3/2) ^(n -1) = -1 *(3/2) ^(n -1)

y1 = - 1  oraz q = 3/2

yn+1 = -1*(3/2) ^n = -1*(3/2)*(3/2)^(n -1) = (3/2) yn

yn+1 = (3/2) yn

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zn = -5/[3^n]

z1 = -5/3

zn+1 = -5/[ 3^(n +1)] = -5/[ 3^n   * 3] = (1/3) *[-5/ 3^n]

zn=1 = (1/3) zn

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