In a geometric sequence, the first term, a1, is equal to 1 , and the fourth term, a4, is equal to 27 . 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 1 , and the fourth term, a4, is equal to 27 . 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=1 and the fourth term a4=27.
Use Formula for nth Term: Use the formula for the nth term of a geometric sequence to find the common ratio.The formula for the nth term of a geometric sequence is an=a1⋅r(n−1), where r is the common ratio.
Substitute Given Terms: Substitute the given terms into the formula to create an equation.We know that a4=a1×r4−1, which simplifies to 27=1×r3.
Solve for Common Ratio: Solve for the common ratio r. Since 27=r3, we can find r by taking the cube root of 27. r=271/3r=3
More problems from Convert a recursive formula to an explicit formula