Question

Jeżeli (an) jest ciągiem geometrycznym , w którym a5=1 i a7= 16 to ile bedzie a6?

Answer 1

a5=1

a7=16

 

a1*q⁴=1   -> a1=1/q⁴

a1*q⁶=16

 

1/q⁴*q⁶=16

1q²=16 /√

q=4  lub q=-4

 

a6= -4 lub a6=4

 

a1 = a5/ q^4 = 1 /256

a6 = a1*q^5 = [ 1/256]*( -4)⁵ = -4

lub

a6 = [1/256]* 4⁵ = 4

 

 

Answer 2

a5 = 1  

 a7 = 16

a5 = a1*q^4 

 a7 = a1*q^6

więc:

a7 : a5 = q^2 = 16 

  q = - 4  lub  q = 4

a1 = a5/ q^4 = 1 /256

a6 = a1*q^5 = [ 1/256]*( -4)^5 = -4

lub

a6 = [1/256]* 4^5 = 4

odp:

a6=-4 lub  a6=4