Question

2) Escribe los 10 primeros términos de una progresión geométrica de razón r = 1/3 y
a5 = 2.

Answer 1

r = 1/3
a5 = 2
n = 5

an = a1*r^(n-1)
2 = a1*(1/3)^(5-1)
2 = a1*1/3^4
2 = a1 * 1/81
a1 = 2*81
a1 = 162

Los demás términos son:

a2 = a1*r^(2-1) = 162*(1/3)^(1) = 162*1/3 = 54
a3 = a1*r^(3-1) = 162*(1/3)^(2) = 162*1/9 = 18
a4 = a1*r^(4-1) = 162*(1/3)^(3) = 162*1/27 = 6
a5 = a1*r^(5-1) = 162*(1/3)^(4) = 162*1/81 = 2
a6 = a1*r^(6-1) = 162*(1/3)^(5) = 162*1/243 = 2/3
a7 = a1*r^(7-1) = 162*(1/3)^(6) = 162*1/729 = 2/9
a8 = a1*r^(8-1) = 162*(1/3)^(7) = 162*1/2187 = 2/27
a9 = a1*r^(9-1) = 162*(1/3)^(8) = 162*1/6561 = 2/81
a10 = a1*r^(10-1) = 162*(1/3)^(9) = 162*1/19683 = 2/243