Question

1)wyznacz ciąg geometryczny,jeśli a2=8 a5=64

2)wyznacz ciąg arytmetyczny jeśli a5=16 a7=40

Answer 1

 

1)

a₂ = 8

a₅ = 64

 

 

 

a₂ = a₁ x q

a₅ = a₁ x q⁴

 

a₁ x q = 8 => a₁ = 8/q

a₁ x q⁴ = 64

 

8/q x q⁴ = 64

8 x q³ = 64

q³ = 8

q = 2

 

a₁ x 2 = 8

a₁ = 4

 

a₁ = 4

q = 2

 

an = 4 x 2^(n-1)

 

2)

a₅ = a₁ + 4r = 16

a₇ = a₁ + 6r = 46

 

a₁ + 4r = 16

a₁ + 6r = 46

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2r = 30

r = 15

 

a₁ + 4*15 = 16

a₁ + 60 = 16

a₁ = -44

 

an = -44 + 15(n-1) = -44 + 15n - 15 = -59 + 15n

 

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Answer 2

1.

a2 = 8 ,  a5 = 64     ciąg geometryczny 

 

q³ = a5/a2 = 64/8  = 8

q = ∛8 = 2

a2 = q*a1  /:q

2a1 = 8  /:2

a1 = 4

 

 

an = a1 * q^(n-1)

an = 4 *2^(n-1)

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2.

a5 = 16,  a7 = 40     ciąg arytmetyczny

 

a5 = a1 + 4r = 16

a7 = a1 + 6r = 46

 

6r - 4r = 46 - 16

2r = 30  /:2

r = 15

a1 + 4*15 = 16

a1 = 16 - 60

a1 = -44

 

an = a1 + (n-1)*r

an = -44 + (n-1) *15 = -44 + 15n - 15

an = 15n - 59

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