find the two geometric means between 3 and 768
Answer (1)
he sequence is 3, x_{1}, x_{2}, x_{3}, 768 The formula for the geometric mean between two numbers a and b is given by \sqrt{a \cdot b} The total number of terms is 5, so the common ratio r can be found using the formula r =[4]{768}{3}}Calculate:{768}{3} = 256 Find r =:[4]{256} = 4 Now, calculate the geometric means:x_{1} = 3 \ r = 3 \ 4 = 12 x_{2} = x_{1} \ r = 12 \ 4 = 48 x_{3} = x_{2} \ r = 48 \4 = 192
