In a geometric sequence, the first term, a_(1), is equal to 8 , and the third term, a_(3), is equal to 72 . Which number represents the common ratio of the geometric sequence? r=2 r=3 r=4 r=5

Question

In a geometric sequence, the first term,  a_(1), is equal to 8 , and the third term,  a_(3), is equal to 72 . Which number represents the common ratio of the geometric sequence?  r=2  r=3  r=4  r=5

Bytelearn · Accepted Answer

Understand Geometric Sequences: Understand the properties of a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio (r). The nth term of a geometric sequence can be found using the formula a_(n) = a_(1) * r^(n-1), where a_(1) is the first term and a_(n) is the nth term.Set Up Equation for Common Ratio: Set up the equation to find the common ratio using the given terms. We are given the first term a_(1) = 8 and the third term a_(3) = 72. We can use the formula for the nth term of a geometric sequence to write the equation for the third term: a_(3) = a_(1) * r^(3-1) = 8 * r^2.Substitute Known Values: Substitute the known values into the equation. 72 = 8 * r^2Solve for Common Ratio: Solve for the common ratio (r). Divide both sides of the equation by 8 to isolate r^2. 72 / 8 = r^2 9 = r^2Find Value of r: Find the value of r by taking the square root of both sides. r = sqrt(9) r = 3 or r = -3Determine Appropriate r: Determine the appropriate value of r. Since we are looking for a common ratio in a geometric sequence, and the sequence is typically considered with positive terms, we take r = 3 as the common ratio.

In a geometric sequence, the first term, $a_{1}$ , is equal to $8$ , and the third term, $a_{3}$ , is equal to $72$ . Which number represents the common ratio of the geometric sequence? $\newline$ $r=2$ $\newline$ $r=3$ $\newline$ $r=4$ $\newline$ $r=5$

Full solution

More problems from Find the sum of a finite geometric series

Related topics

In a geometric sequence, the first term, a1 a_{1} a1​, is equal to 888 , and the third term, a3 a_{3} a3​, is equal to 727272 . Which number represents the common ratio of the geometric sequence?\newliner=2 r=2 r=2\newliner=3 r=3 r=3\newliner=4 r=4 r=4\newliner=5 r=5 r=5

In a geometric sequence, the first term, $a_{1}$ , is equal to $8$ , and the third term, $a_{3}$ , is equal to $72$ . Which number represents the common ratio of the geometric sequence? $\newline$ $r=2$ $\newline$ $r=3$ $\newline$ $r=4$ $\newline$ $r=5$