Question

Proszę o rozwiązanie zadań 1, 2, 3, 4, 9, 10 z załącznika. Dam najlepszą odp.

Answer 1

1/

a1 = 4

s3 = 27

 

s3 = a1 + a2 + a3

s3 = a1 + a1 + r + a1 + 2*r

 

27 = 4 + 4 + 4 + 3r

3r = 15

r = 5

 

 

2/

q = 4

s4 = 255

 

a1 + a1*q + a1*q*q + a1*q*q*q = 255

a1 + 4a1 + 16a1 + 64a1 = 255

85a1 = 255

a1 = 3

 

 

3/

x², 2x, 3

 

x² + r = 2x

2x + r = 3

 

r = 2x - x²

2x + 2x - x² = 3

x² -4x + 3 = 0

(x-1)(x-3) = 0

x=1 lub x=3

 

 

4/

3, x+1, 12

 

3*q = x+1

(x+1)*q = 12

 

3q * q = 12

q² = 4

q=2 lub q=-2

x=3q-1

x=5 lub x=-7

 

 

9/

a1-a2 = -2 = r

a2 = -4

a2 = a1 + r

a1 = a2 - r = -4 + 2 = -2

a10 = a1 + 9*r = -2 -18 = -20

 

suma = 10 * (a1 + a10)  / 2 = 10 * (-2 - 20) / 2 = 5*-22 = -110

 

 

10/

a4 = 24

a1 = 3

 

a4 = a1 * q * q * q

24 = 3* q³

q = 2

 

suma = a1 * (1-q^10) / (1-q) = 3*(1-2^10)/-1 = -3*(1-1024) = 3*1023 = 3069