ssume that the pattern of a square followed by 2 circles and a triangle continue
ID: 3197448 • Letter: S
Question
ssume that the pattern of a square followed by 2 circles and a triangle continues to repeat in the se- quence of shapes in Figure 9.49 and that the num- bers below the shapes indicate the position of each numbers form: an arithmetic sequence. a geo- metric sequence, or neither? Why? If it is either an arithmetic sequence or a geometric sequence give an expression for the Nth entry shape in the sequence d. Consider the numbers that are below the circles. a, what shape will be above the number 150? What kind of sequence do these numbers form: an arithmetic sequence, a geometric sequence or neither? Why? If it is either an arithmetic se- quence or a geometrie sequence, give an expres- sion for the Nth entry Explain how you can tell. b. How many circles will there be above the numbers 1 through 150? Explain your answer c. Consider the numbers that are below the squares. What kind of sequence do these 23 456781 1 12 13 14 15 16 Figure 2.49 A repeating patern of shapesExplanation / Answer
(a)
the shapes are repeating after every 4 numbers so we will divide 150 by 4
150 = 37*4 + 2
so at 150 you will have the shape you have at 2 i.e. Circle
answer is circle
(b)
As you can see there are 37 times repetition of these 4 shapes happen from 1 to 148.
at 149, there is a square and at 150, there is a circle
in every repetition, there are 2 circles.
so there are in total = 37*2 + 1 = 75 circles
alternate method -
In every 2 numbers, there is 1 circles, so in 150 numbers, there will be 75 circles.
(c)
squares are occuring at 1, 5, 9, 13...
this is an arithmetic sequence with common difference of 4.
(d)
circles are occuring at 2,3,6,7,10,11...
these are 2 arithmetic sequences -
1. first term 2 and common difference 4
2. first term 3, and common difference 4
please upvote the answer.
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