Pergunta

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 3,6,12,ldots Answer Attemptiout of a This is square sequence and the square is equal to
Solução

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GustavoAvançado · Tutor por 1 anos
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if the sequence is arithmetic or geometric, we need to check if there is a constant difference or ratio between consecutive terms.<br /><br />In this case, the sequence is $3, 6, 12, \ldots$.<br /><br />Let's check if it is an arithmetic sequence by finding the difference between consecutive terms:<br /><br />$6 - 3 = 3$<br />$12 - 6 = 6$<br /><br />Since the differences are not constant, the sequence is not arithmetic.<br /><br />Now let's check if it is a geometric sequence by finding the ratio between consecutive terms:<br /><br />$\frac{6}{3} = 2$<br />$\frac{12}{6} = 2$<br /><br />Since the ratios are constant, the sequence is geometric.<br /><br />The common ratio in simplest form is $2$.<br /><br />Therefore, the sequence $3, 6, 12, \ldots$ is a geometric sequence with a common ratio of $2$.
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