Question

Qual o número de termos da PG (400, 40, ... 4/100 )

Answer 1

a1 = 400
an = 4/100 ou 1/25
n = ?
q = 1/10

an = a1 . q^n-1
4/100 = 400 . 1/10^n-1 
4/100/400 = 1/10^n-1
4/40000 = 1/10^n-1
1/10000 = 1/10^n-1
log 1/10000 = log 1/10^n-1
log 1/10000 = n-1 . log 1/10
log 0,0001 = n - 1 . log 0,1
n - 1 = log 0,0001/log 0,1
n - 1 = 4
n = 4 + 1
n = 5