Question

Mariana é professora de Educação Física e, em um dos seus treinamentos de alta performance, programou uma sequência de corridas. Ela deve correr 7 dias e, a cada dia, precisa percorrer uma distância igual ao dobro da distância que correu no dia anterior. No primeiro dia desse treinamento, Mariana deve correr 200 metros.

Answer 1

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Explicação passo a passo:

Answer 2

Mariana deve correr 12.800 metros no último dia de treinamento.

Progressão geométrica

Uma progressão geométrica é caracterizada por uma sequência de valores crescentes, decrescentes ou alternados, onde a razão entre um valor e seu antecessor é sempre constante. O termo geral da P.G. é dado por aₙ = a₁·qⁿ⁻¹, sendo q a razão calculada por q = aₙ₊₁/aₙ.

Para resolver a questão, precisamos calcular a distância percorrida no último dia de treinamento. Se a distância deve ser sempre o dobro do dia anterior, a razão da PG será igual a 2. Como o primeiro termo é 200, temos:

aₙ = 200·2ⁿ⁻¹

Para o sétimo dia, teremos n = 7:

a₇ = 200·2⁷⁻¹

a₇ = 200·64

a₇ = 12.800 metros

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