find the numbers of this geometric sequence: 8, __ , __, __, 648
8, 8r, 8r^2, 8r^3, 8r^4
but 8r^4 = 648
r^4 = 81
r = ± 3
you have either
8, 24, 72, 216, 648
or
8, -24, 72, -216, 648
The common ratio is (648/8)^(1/4) = 3
8*3=24
24*3=72
72*3=216
216*3=648
To find the missing numbers in this geometric sequence, we need to determine the common ratio.
The common ratio (r) can be found by dividing any term in the sequence by its preceding term.
Let's find the common ratio using the first two terms:
r = 8 ÷ 8 = 1
Therefore, the common ratio (r) for this sequence is 1.
To find the missing terms, we will multiply each term by the common ratio:
Term 1: 8
Term 2: 8 × r = 8 × 1 = 8
Term 3: 8 × r × r = 8 × 1 × 1 = 8
Term 4: 8 × r × r × r = 8 × 1 × 1 × 1 = 8
Term 5: 8 × r × r × r × r = 8 × 1 × 1 × 1 × 1 = 8
So, the missing terms in the geometric sequence are:
8, 8, 8, 8, 648
To find the numbers of a geometric sequence, we need to determine the common ratio.
In this case, we can find the common ratio by dividing any term by its previous term. Let's take the second term and divide it by the first term:
Second term / First term = __ / 8
We are missing this value, so we can call it "x."
So, x / 8 is equal to the common ratio.
Next, we divide the third term by the second term:
Third term / Second term = __ / x
Similarly, dividing the fourth term by the third term gives us:
Fourth term / Third term = __ / (__ / x)
Finally, dividing the fifth term by the fourth term gives us the following equation:
Fifth term / Fourth term = 648 / (__ / __)
To solve for the missing values, we can set up a proportion using these equations:
x / 8 = __ / x = __ / (__ / x) = 648 / (__ / __)
By solving this proportion, we can find the missing numbers in the geometric sequence.