Pergunta

Which formula is used to find the explicit equation for geometric sequences? a) a_(n)=a_(n-1)+d b) a_(n)=a_(n-1)ast r C) a_(n)=a_(1)+d(n-1) d) a_(n)=a_(1)ast r^n-1
Solução

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VanessaProfissional · Tutor por 6 anos
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The correct answer is d) $a_{n}=a_{1}\ast r^{n-1}$.<br /><br />In a geometric sequence, each term is obtained by multiplying the previous term by a constant called the common ratio (r). The explicit formula for a geometric sequence is given by $a_{n}=a_{1}\ast r^{n-1}$, where $a_{n}$ represents the nth term, $a_{1}$ is the first term, and r is the common ratio.<br /><br />Option a) represents the recursive formula for an arithmetic sequence, where each term is obtained by adding a constant difference (d) to the previous term.<br /><br />Option b) is incorrect as it does not represent any standard formula for sequences.<br /><br />Option c) represents the explicit formula for an arithmetic sequence, where each term is obtained by adding a constant difference (d) to the first term.<br /><br />Therefore, the correct formula for finding the explicit equation for geometric sequences is d) $a_{n}=a_{1}\ast r^{n-1}$.
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