Question

Quantos termos tem essa PG​

Answer 1

Resposta:

5 termos

Explicação passo-a-passo:

Primeiro vou descobrir a razão

$q = \frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times 2 = \frac{6}{4} = \frac{3}{2}$

Termo geral

$an = a1 \times q {}^{n - 1}$

$\frac{81}{32} = \frac{1}{2} \times ( \frac{3}{2}) {}^{n - 1} \: \: \: \: ( \times 2) \\ 2 \times \frac{81}{32} = 2 \times \frac{1}{2} \times ( \frac{3}{2} ) {}^{n - 1} \\ \frac{81}{16} = ( \frac{3}{2}) {}^{n - 1} \\ ( \frac{3}{2} ) {}^{4} = ( \frac{3}{2}) {}^{n - 1} \\ 4 = n - 1 \\ n = 4 + 1 \\ n = 5$