Use the recursively defined geometric sequence a1=5/6 , an=4an−1 and find the common ratio.(1 point) Responses 10/3 Start Fraction 10 over 3 End Fraction −2/3 negative Start Fraction 2 over 3 End Fraction 5/6 Start Fraction 5 over 6 End Fraction 4 4
To find the common ratio in a geometric sequence, we divide each term by its previous term.
Let's divide the second term ($a_2$) by the first term ($a_1$):
$a_2 / a_1 = (4a_1) / a_1 = 4$
Similarly, let's divide each subsequent term ($a_n$) by its previous term ($a_{n-1}$):
$a_3 / a_2 = (4a_2) / a_2 = 4$
$a_4 / a_3 = (4a_3) / a_3 = 4$
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In a geometric sequence, the common ratio is the same for each term, so we can conclude that the common ratio is 4.