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Step-by-step explanation:
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we have the equation a(n) = (1/2)n - 1 for n ≥ 1
First we need the first five terms:
a(1) = (1/2)*1 - 1 = -1/2
a(2) = (1/2)*2 - 1 = 0
a(3) = (1/2)*3 - 1 = 1/2
a(4) = (1/2)*4 - 1 = 1
a(5) = (1/2)*5 - 1 = 3/2
then we can see that each term is 1/2 bigger than the previous one, then a recursive relation can be written as:
a(n) = a(n-1) + 1/2
where n ≥ 2, and a(1) = -1/2
First, you divide the 2 yard spool into 5 equal lengths, or perform the operation 2/5.
After completing this, you get that each length of ribbon is 0.4 yards. But the question asks for it in feet. (There are 3 feet in a yard) Therefore, we must multiply the number of yards by 3, to find this number in feet.
0.4*3= 1.2
Therefore, the 5 equal lengths of ribbon measure 1.2 feet.
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