Calculate the missing terms of the geometric sequence…3072,?,?,?,12
To find the missing terms of the geometric sequence, we need to determine the common ratio.
The common ratio (r) can be found by dividing any term in the sequence by the previous term.
For example, if we divide the second term of the sequence by the first term, we have the equation:
? / 3072 = r
Similarly, dividing the third term by the second term gives:
? / ? = r
And dividing the fourth term by the third term gives:
12 / ? = r
Since we know the last term is 12, we can write the equation:
12 / ? = r
To find some common ratio r, we can evaluate the ratio between any two consecutive terms. Let's choose to evaluate the ratio between the third and second terms.
? / ? = r
(?) / 3072 = r
We also know that the last term is 12:
12 / ? = r
Since these two expressions are both equal to r, they are equal to each other:
(?) / 3072 = 12 / ?
To solve for ?, we can cross-multiply:
(?) * ? = 3072 * 12
?^2 = 36864
Taking the square root of both sides:
? = ± √(36864)
Since ? cannot be negative in a geometric sequence, we have:
? = 192
Now, we can fill in the missing terms of the geometric sequence:
3072, 192, 12