Question

Wyznacz liczbę n w ciągu geometrycznym(an) jeśli; a) a1=25 an=12 800 q=2 b) a4=0,5 an−1=0,125 g=−0,5

Answer 1

a)

a1 = 25

an = 12 800

q = 2

 

an = a1* q^(n-1)

zatem

25*2^(n -1) = 12 800 / : 25

2^(n -1) = 512

2^( n -1) = 2^9

n -1 = 9

n = 10

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b)

a4 = 0,5= 1/2

an-1 = 0,125 = 1/8

q = - 0,5 = - 1/2

 

a4 = a1 * q^3

czyli

a1* ( -1/2)^3 = 1/2

a1*( - 1/8) = 1/2

a1 = ( 1/2)* (-8) = - 4

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an-1 = a1 *q^( n -2)

( -4)*( -1/2)^( n -2) = 1/8  / : ( -4)

( -1/2)^( n -2) = - 1/32 = ( -1/2)^5

n -2 = 5

n = 7

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