In a geometric sequence, the first term, a1, is equal to 2 , and the fourth term, a4, is equal to 128 . 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 2 , and the fourth term, a4, is equal to 128 . 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 2 and the fourth term a4 as 128. We need to find the common ratio r.
Use nth Term Formula: Use the formula for the nth term of a geometric sequence to express the fourth term.The nth term of a geometric sequence is given by an=a1⋅rn−1. For the fourth term, the formula is a4=a1⋅r4−1=a1⋅r3.
Substitute Known Values: Substitute the known values into the formula.We know that a1=2 and a4=128. So, we have 128=2×r3.
Solve for Common Ratio: Solve for the common ratio r. Divide both sides of the equation by 2 to isolate r3. 128/2=r364=r3
Find Cube Root: Find the cube root of 64 to solve for r.The cube root of 64 is 4, so r=4.
More problems from Find the sum of a finite geometric series