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In a geometric sequence, the first term,
a_(1), is equal to 4 , and the third term,
a_(3), is equal to 144 . Which number represents the common ratio of the geometric sequence?

r=5

r=6

r=7

r=8

In a geometric sequence, the first term, $a_{1}$ , is equal to $4$ , and the third term, $a_{3}$ , is equal to $144$ . Which number represents the common ratio of the geometric sequence? $\newline$ $r=5$ $\newline$ $r=6$ $\newline$ $r=7$ $\newline$ $r=8$

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Scale drawings: word problems

Full solution

Q. In a geometric sequence, the first term,

a_{1}

, is equal to

4

, and the third term,

a_{3}

, is equal to

144

. Which number represents the common ratio of the geometric sequence?

\newline

r=5

\newline

r=6

\newline

r=7

\newline

r=8

Identify Given Terms: Identify the given terms in the geometric sequence. We are given the first term $a_{1} = 4$ and the third term $a_{3} = 144$ . We need to find the common ratio $r$ .
Write Formula for nth Term: Write the formula for the nth term of a geometric sequence. $\newline$ The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Apply Formula to Given Terms: Apply the formula to the given terms. $\newline$ We know that $a_{3} = a_{1} \cdot r^{3-1} = a_{1} \cdot r^2$ . We can substitute the given values to find $r$ . $\newline$ $144 = 4 \cdot r^2$
Solve for Common Ratio: Solve for the common ratio $r$ . Divide both sides of the equation by $4$ to isolate $r^2$ . $144 / 4 = r^2$ $36 = r^2$
Take Square Root: Take the square root of both sides to solve for $r$ . $r = \sqrt{36}$ $r = 6$

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