Create a sequence with five terms based on the given information. a. A arithmetic sequence with a third term of 8 and a constant
1 answer:
Part a .
A arithmetic sequence with a third term of 8 and a common difference of 5 .
To find the first five therms, since the common difference is 5, so we add 5 to get the fourth term and add 5 to fourth term to get the fifth term .
And for first two terms, we will subtract 5 from 8 to get the second term and subtract 5 from the second term to get the first term. And we will get
Part b:A geometric sequence with a fifth term of 1/3 and constant ratio of 1/3.
TO find the first five terms, since the constant ratio of 1/3, so we multiply 1/3 to third term to get fourth term, and multiply fourth term by 1/3 to get fifth term .
And to get the first two terms, we will divide third term by 1/3, to get the second term and divide the second term by 1/3 to get the first term, that is
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The number of white and grey blocks in the quilts follows a sequence given by the Design number of the quilt
The numbers and patterns of the blocks are;
a. Patterns;
- The height of the white blocks is the Design number, while the rows are one more than the design number
- The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number
b. The function is
c. The function is
d.
e. The design chosen is <u>Design 9</u>
The number of blocks is <u>132 blocks</u>
Reasons:
The pattern of the design are;
a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks
Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks
The number of white blocks in a design, <em>n</em> is the product of <em>n</em> and (n + 1)
The number of grey blocks in a design <em>n</em>, is the product of (n + 2) and (n + 3) less the number of white blocks in the design
b. Based on the above, the function that represent the number of picture blocks in Design <em>n</em>, is therefore;
- p(n) = n·(n + 1)
c. Based on the above, the function that represent the number of border blocks in Design <em>n</em>, is therefore;
- b(n) = (n + 2)·(n + 3) - n·(n + 1)
d. The total number of blocks, t(n) = (n + 2)·(n + 3)
t(n) = (n + 2)·(n + 3) - n·(n + 1) + n·(n + 1)
- t(n) = p(n) + b(n)
e. The given number of picture blocks = 90
The number of picture blocks in a design, n = n × (n + 1)
Therefore, given that the number of picture blocks is 90, we have;
90 = n × (n + 1)
n² + n - 90 = 0
(n + 10)·(n - 9) = 0
n = 9, or n = -10
Therefore, the design museum chooses is <u>Design 9</u>
The total number of blocks in a quilt design, t(n) = (n + 2)·(n + 3)
Total blocks in the design the art museum choses, t(9), is given as follows;
t(9) = (9 + 2)·(9 + 3) = <u>132 blocks</u>
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