2015 Se sabe que la secuencia an y bn satisfacen a1=2 y b1=1.

a2=1 d

a4=1 3d

a3=1 2d

b3=q^2

b2=q

b4=q^3

Entonces 1 D 1 3D = Q 2, 2 4d = Q 2.

q^4=1 2d

Dividir

(2 4d)/(1 2d)=q^2/q^4

q^2=1/2

d=(q^2-2)/4=-3/8

q= √2/2

an = 1 (n-1)* 1/2 = n 1/2

bn=b1*q^(n-1)=( √2/2)^(n-1 )

s 10 =(a 1 a 10)* 10/2 =(a 1 a 1 9d)* 10/2 =(2-27/8)* 5 =-55/8

t10=b1*(1-q^10)/(1-q)=1*[1-(1/2)^5]/(1√2/2)=(62 31√2 ) /32