find the missing terms for the following sequence
geometric sequence
96,__,__,__,6
well, 6 is 96/16, so r = 1/2
To find the missing terms in a geometric sequence, we need to identify the common ratio first. In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio.
Looking at the given sequence: 96, __, __, __, 6
To find the common ratio, we can divide any term in the sequence by its previous term:
Second term / First term = Third term / Second term = Fourth term / Third term = Fifth term / Fourth term = Common Ratio
Let's calculate the common ratio using the first and second terms:
Second term / First term = x / 96
From the problem, we know that the fifth term is 6, so:
Fifth term / Fourth term = 6 / Fourth term
Now we have two equations:
x / 96 = 6 / Fourth term (Equation 1)
6 / Fourth term = 6 / 6 (Equation 2)
Simplifying Equation 2, we get:
1 / Fourth term = 1 / 1
This means the fourth term is 1.
Now we can substitute the value of the fourth term (1) into Equation 1:
x / 96 = 6 / 1
By cross-multiplying, we find:
x = 96 * 6
Calculating the value of x:
x = 576
Therefore, the missing terms in the geometric sequence 96, __, __, __, 6 are 576, 96, 16.