In a geometric sequence, the first term, a_(1), is equal to 1 , and the third term, a_(3), is equal to 36 . 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 1 , and the third term,  a_(3), is equal to 36 . 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)) and the third term (a_(3)) of the geometric sequence. The first term is 1 (a_(1) = 1) and the third term is 36 (a_(3) = 36).Write nth Term Formula: Write the formula for the nth term of a geometric sequence. The nth term of a geometric sequence is given by a_(n) = a_(1) * r^(n-1), where a_(1) is the first term and r is the common ratio.Express Third Term: Use the formula to express the third term in terms of the first term and the common ratio. We have a_(3) = a_(1) * r^(3-1) = a_(1) * r^2.Substitute Given Values: Substitute the given values into the equation. We know that a_(1) = 1 and a_(3) = 36, so we can write 36 = 1 * r^2.Solve for Common Ratio: Solve for the common ratio r. To find r, we take the square root of both sides of the equation: r^2 = 36, so r = ±√36.Determine Positive Ratio: Determine the positive value of the common ratio. Since a common ratio in a geometric sequence is typically positive, we take the positive square root of 36, which is 6. Therefore, r = 6.

In a geometric sequence, the first term, $a_{1}$ , is equal to $1$ , and the third term, $a_{3}$ , is equal to $36$ . 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, a1 a_{1} a1​, is equal to 111 , and the third term, a3 a_{3} a3​, is equal to 363636 . Which number represents the common ratio of the geometric sequence?\newliner=3 r=3 r=3\newliner=4 r=4 r=4\newliner=5 r=5 r=5\newliner=6 r=6 r=6

In a geometric sequence, the first term, $a_{1}$ , is equal to $1$ , and the third term, $a_{3}$ , is equal to $36$ . Which number represents the common ratio of the geometric sequence? $\newline$ $r=3$ $\newline$ $r=4$ $\newline$ $r=5$ $\newline$ $r=6$