1. Calcule quantos elementos tem essas P.Ga.) a1=9 , an=3 elevado a 20 e q=3b.) an=1875 , a1=3 e q= .... Pergunta de ideia deFilomena171

August 2019 1 62 Report

1. Calcule quantos elementos tem essas P.G

a.) a1=9 , an=3 elevado a 20 e q=3

b.) an=1875 , a1=3 e q= 5.

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emicosonia 1. Calcule quantos elementos tem essas P.G
n = elementos

a.) a1=9 , an=3 elevado a 20 e q=3

DEIXAR bases IGUAIS
FÓRMULA da PG

an = a1.q^(n - 1)
3²º = 9.3^(n - 1) ( lembrando que 9 = 3x3 = 3²)
3²º = 3².3^(n - 1) mesmo que

3².3^(n - 1) = 3²º

3²º
3^(n - 1) = ----------
3²

3²(3¹⁸)
3^(n - 1) = ---------- elimina AMBOS (3²)
3²(1)

3¹⁸
3^(n- 1) = -------
1

3^(n - 1) = 3¹⁸ mesma BASE (3))

(n - 1) = 18
n - 1 = 18
n = 18 + 1
n = 19 ( elementos)

b.) an=1875 , a1=3 e q= 5.

an = a1.q^(n - 1)
1875 = 3.5^(n - 1) mesmo que

3.5^(n - 1) = 1875

5^(n- 1) = 1875/3
5^(n - 1)= 625 ( 625 = 5x5x5x5 = 5⁴)

5^(n - 1) = 5⁴ (mesma BASE)(5))

(n - 1) = 4
n - 1 = 4
n = 4 + 1
n = 5 ( elementos)

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