In a geometric sequence, the first term, a1, is equal to 7 , and the fifth term, a5, is equal to 112 . Which number represents the common ratio of the geometric sequence?r=1r=2r=3r=4
Q. In a geometric sequence, the first term, a1, is equal to 7 , and the fifth term, a5, is equal to 112 . Which number represents the common ratio of the geometric sequence?r=1r=2r=3r=4
Identify Given Terms: Identify the given terms in the geometric sequence.We are given the first term a1 as 7 and the fifth term a5 as 112.
Recall Formula: Recall the formula for the nth term of a geometric sequence.The nth term of a geometric sequence is given by an=a1⋅r(n−1), where r is the common ratio.
Set Up Equation: Set up the equation to find the common ratio using the given terms.We have a5=a1×r5−1, which simplifies to 112=7×r4.
Solve for Ratio: Solve for the common ratio r.Divide both sides of the equation by 7 to isolate r4.7112=r416=r4
Find Fourth Root: Find the fourth root of 16 to solve for r. r=1641r=2
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