Question

Determine quantos termos tem a PG (4,20,100,...,12500)

Answer 1

q = 20/4 = 5

an = a1 * q^n-1
12 500 = 4 * 5^n-1
3 125 = 5^n-1
5^5 = 5^n-1
n-1 = 5
n = 5 + 1
n = 6 termos.

Answer 2

an=a1.q^n-1

 an=12500 a1=4 q= razão entre a2 e a1= 20/4= 5

12500=4.5^n-1
12500/4=5^n-1
3125=5^n-1                    decompor o 3125 = 5^5
5^5=5^n-1
corta as bases
5=n-1
5+1=n
6=n

n= número de termos
6=n