In a geometric sequence, the first term, a1, is equal to 1 , and the third term, a3, is equal to 9 . Which number represents the common ratio of the geometric sequence?r=2r=3r=4r=5
Q. In a geometric sequence, the first term, a1, is equal to 1 , and the third term, a3, is equal to 9 . Which number represents the common ratio of the geometric sequence?r=2r=3r=4r=5
Understand Geometric Sequence Properties: 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 an=a1×r(n−1), where a1 is the first term and r is the common ratio.
Set Up Common Ratio Equation: Set up the equation to find the common ratio using the given terms.We know that a1=1 and a3=9. Using the formula for the nth term of a geometric sequence, we can write the equation for the third term as follows:a3=a1×r3−19=1×r2
Solve for Common Ratio: Solve for the common ratio r. Now we simplify and solve for r: 9=r2 To find r, we take the square root of both sides of the equation: r=9r=3
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