In a geometric sequence, the first term, a_(1), is equal to 6 , and the third term, a_(3), is equal to 96 . Which number represents the common ratio of the geometric sequence? r=3 r=4 r=5 r=6

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In a geometric sequence, the first term,  a_(1), is equal to 6 , and the third term,  a_(3), is equal to 96 . Which number represents the common ratio of the geometric sequence?  r=3  r=4  r=5  r=6

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Identify Given Terms: Identify the given terms in the geometric sequence. We are given the first term (a_(1)) as 6 and the third term (a_(3)) as 96. In a geometric sequence, each term is found by multiplying the previous term by the common ratio (r).Write Formula for Third Term: Write the formula for the third term of a geometric sequence. The third term (a_(3)) can be expressed in terms of the first term (a_(1)) and the common ratio (r) as follows: a_(3) = a_(1) * r^2Substitute Known Values: Substitute the known values into the formula. We know that a_(1) = 6 and a_(3) = 96, so we can substitute these values into the formula: 96 = 6 * r^2Solve for Common Ratio: Solve for the common ratio (r). To find r, we need to divide both sides of the equation by 6: r^2 = 96 / 6 r^2 = 16Take Square Root: Take the square root of both sides to solve for r. Since r^2 = 16, we find that r can be either positive or negative square root of 16. However, since a common ratio is typically positive in the context of geometric sequences, we will consider the positive square root: r = √16 r = 4

In a geometric sequence, the first term, $a_{1}$ , is equal to $6$ , and the third term, $a_{3}$ , is equal to $96$ . Which number represents the common ratio of the geometric sequence? $\newline$ $r=3$ $\newline$ $r=4$ $\newline$ $r=5$ $\newline$ $r=6$

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In a geometric sequence, the first term, $a_{1}$ , is equal to $6$ , and the third term, $a_{3}$ , is equal to $96$ . Which number represents the common ratio of the geometric sequence? $\newline$ $r=3$ $\newline$ $r=4$ $\newline$ $r=5$ $\newline$ $r=6$