Need to get these problems checked--
31. Determine whether the sequence 7, 21, 35, 49 is geometric. If so, find its common ratio.
a. no
b. yes, common ratio of 14
c. yes, common ratio of 12
I'm stuck between A and B..
32. What are the next three terms of the geometric sequence 5, 15, 45,...?
135, 405, 1215? Not sure about this...
33. What is the area of a square with the dimension of 1 + sqrt of 2?
9.64?
35. Simplify: 2 sqrt of 4 + 2 sqrt of 8
4+ 5.65?
Thanks
-MC
31. How are you stuck? There is how much between each number? Take two consecutive numbers and subtract them.\
32. Correct
33. Not sure
35. 2sqrt4+2sqrt8=4+4sqrt2
So 31 is B?
-MC
Let's go through each of the problems and check the solutions:
31. Determine whether the sequence 7, 21, 35, 49 is geometric. If so, find its common ratio.
To check if a sequence is geometric, we need to see if the ratio of any term to the previous term is constant. Let's calculate the ratios for the given sequence:
21/7 = 3
35/21 ≈ 1.6667
49/35 ≈ 1.4
Since the ratios are not equal, the sequence is not geometric. Thus, the correct answer is option A - no.
32. What are the next three terms of the geometric sequence 5, 15, 45,...?
In a geometric sequence, each term is found by multiplying the previous term by a constant ratio. In this case, the common ratio can be found by dividing any term by its previous term:
15/5 = 3
Now, we can use this common ratio to find the next terms:
45 * 3 = 135
135 * 3 = 405
405 * 3 = 1215
Therefore, the next three terms of the geometric sequence are 135, 405, 1215.
33. What is the area of a square with the dimension of 1 + sqrt(2)?
To find the area of a square, we need to square one of its sides. In this case, the side length is 1 + sqrt(2). So, we square this value:
(1 + sqrt(2))^2 = 1 + 2sqrt(2) + 2
= 3 + 2sqrt(2)
Thus, the area of the square is 3 + 2sqrt(2).
35. Simplify: 2sqrt(4) + 2sqrt(8)
To simplify this expression, we need to simplify the square roots of the numbers within each term:
2sqrt(4) = 2 * 2 = 4
2sqrt(8) = 2 * sqrt(4) * sqrt(2) = 4sqrt(2)
Now, we can combine the simplified terms:
4 + 4sqrt(2)
Therefore, the simplified form of 2sqrt(4) + 2sqrt(8) is 4 + 4sqrt(2).
I hope this helps!