Calculate the missing terms of the geometric sequence ..., 2048, ?, ?, ?, 8, ... Select all that apply.
1,538, 1,028, 518 *****
1,534, 1,020, 514
512, 128, 32
-512, 128, -32
-1,534, 1,020, -514
-1,538, 1,028, -518
I have to pick 2 options. I know the first one is correct, but I don't know how to get another option. Please help? Thanks
you are given a2, a6.
a6=8=2048r^4
r^4=8/2048=
r=+-1/4
2048,512,128,32,8,2....
or r could be -1/4
2048,-512,128,-32,8,-2....
so two answers are right.
r=
2048*1/251=
That's interesting, I was super wrong 0_0 I guess its the middle two...
Wait, is this because this is geometric and not arithmetic? Because I got answer a through adding and doing the mean thing... is that where I went wrong?
Sure, happy to help! To calculate the missing terms of a geometric sequence, we need to find the common ratio (r) between consecutive terms. In this case, we can divide each term by the previous term to find the common ratio.
Let's start with the given sequence: ..., 2048, ?, ?, ?, 8, ...
If we divide 2048 by the previous term (which is also 2048), we get:
2048/2048 = 1
So the common ratio, r, is 1. Now we can use this ratio to find the missing terms.
We know that the first missing term is before 2048, and the second missing term is after 8. Let's calculate them:
To find the term before 2048, we divide 2048 by the common ratio:
2048 / 1 = 2048
So the first missing term is 2048.
To find the term after 8, we multiply 8 by the common ratio:
8 * 1 = 8
So the second missing term is also 8.
Now let's go through the given options and see which ones match the missing terms:
1) 1,538, 1,028, 518:
None of the missing terms match this option.
2) 1,534, 1,020, 514:
None of the missing terms match this option.
3) 512, 128, 32:
None of the missing terms match this option.
4) -512, 128, -32:
None of the missing terms match this option.
5) -1,534, 1,020, -514:
None of the missing terms match this option.
6) -1,538, 1,028, -518:
One missing term (-518) matches this option.
So the correct options are 1) 518 and 6) -518.
To find the missing terms of the geometric sequence ..., 2048, ?, ?, ?, 8, you need to determine the common ratio (r) between the terms.
To find the common ratio, divide any term by its preceding term.
2048 / 8 = 256
So, the common ratio (r) is 256.
Now you can use the common ratio (r) to find the missing terms.
To find the first missing term:
2048 / r = ?
Substituting the value of r:
2048 / 256 = 8
So, the first missing term is 8.
To find the second missing term:
8 / r = ?
Substituting the value of r:
8 / 256 = 1/32
So, the second missing term is 1/32.
Based on these calculations, the missing terms of the sequence are 8 and 1/32.
From the provided options, the correct answers are:
1. 1,538, 1,028, 518
2. -1,538, 1,028, -518
To find the missing terms of a geometric sequence, we need to identify the common ratio (r) between consecutive terms. In this case, we will divide each term by its preceding term. Let's calculate the common ration for the known terms:
2048 ÷ ... = ... ÷ 2048
To determine the missing terms, we divide the known terms by the common ratio (r):
2048 ÷ r = ?, ?, ?, ?, 8
Now let's calculate each option given and see which one fits in the sequence:
Option 1: 2048 ÷ r = 538 ⇒ r = 2048 ÷ 538 ≈ 3.807
Applying the common ratio, we get: 2048 ÷ 3.807 ≈ 538, 2048 ÷ 3.807² ≈ 282, 2048 ÷ 3.807³ ≈ 147
Option 2: 2048 ÷ r = 514 ⇒ r = 2048 ÷ 514 ≈ 3.988
Using the common ratio, we obtain: 2048 ÷ 3.988 ≈ 514, 2048 ÷ 3.988² ≈ 128, 2048 ÷ 3.988³ ≈ 32
Option 3: 2048 ÷ r = 32 ⇒ r = 2048 ÷ 32 = 64
Applying the common ratio, we get: 2048 ÷ 64 ≈ 32, 2048 ÷ 64² = 2, 2048 ÷ 64³ ≈ 0.125
Option 4: 2048 ÷ r = -32 ⇒ r = 2048 ÷ -32 = -64
Using the common ratio, we obtain: 2048 ÷ -64 = -32, 2048 ÷ -64² ≈ 0.5, 2048 ÷ -64³ ≈ -0.0078
Option 5: 2048 ÷ r = -514 ⇒ r = 2048 ÷ -514 ≈ -3.988
Using the common ratio, we obtain: 2048 ÷ -3.988 ≈ -514, 2048 ÷ -3.988² ≈ -128, 2048 ÷ -3.988³ ≈ -32
Option 6: 2048 ÷ r = -518 ⇒ r = 2048 ÷ -518 ≈ -3.956
Applying the common ratio, we get: 2048 ÷ -3.956 ≈ -518, 2048 ÷ -3.956² ≈ -130, 2048 ÷ -3.956³ ≈ -33
From the calculations, option 1 (1,538, 1,028, and 518) fits the geometric sequence. However, option 3 (512, 128, and 32) also fits the sequence. Therefore, the correct answers are options 1 and 3.