Question

Determine o número de termos da PG (9, 3, 1, ..., 1/81)?

Answer 1

Resposta:

Ela tem 7 termos

Explicação passo-a-passo:

$a_n={1\over81}\\ \\ a_1=9\\ n=?\\ r=q=3\div9={3\over9}={1\over3}\\ \\ a_n=a_1.q^{n-1}\\ \\ {1\over81}=9.({1\over3})^{n-1}\\ \\ {1\over81}\div9=({1\over3})^{n-1}\\ \\ {1\over81}\times{1\over9}=({1\over3})^{n-1}\\ \\ {1\over729}=({1\over3})^{n-1}\\ \\( {1\over3})^6=({1\over3})^{n-1}\\ \\ n-1=6\\ n=6+1\\ n=7$