Question

Qual termo do PG (729,2430,8100,...)é igual a 1000000?

Answer 1

an = a1.q^n-1

q = a2/a1
q = 2430/729
q = 10/3

1000000 = 729.(10/3)^n-1
1000000/729 = (10/3)^n / (10/3)
(10/3).(1000000/729) = (10/3)^n
10000000/2187 = (10/3)^n

log (10000000/2187) = log (10/3)^n
log (10000000/2187) = n.log(10/3)

n = log(10000000/2187) / log(10/3)
n = 3.660 15 12 17 / 0. 522878745
n = 7

Logo concluimos que o termo da PG é 7