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Can anyone help me with these problems?

1. A square has a side of 2 decimeters. A new square is formed by joining the midpoints of the sides. If this procedure is repeated 6 times, what is the perimeter and area of the seventh square ?
2. Find the sum of those numbers between 15 and 810 which have 8 as their units digit.
3. In an arithmetic sequence, the sixth term is twice the 3rd term and the 30th term is 60. find the common difference?

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2 answers

  1. #1. Each nested side is 1/√2 as long as the previous side. Use that to find the length of the nth nested side.

    #2. Since the last digit is 8, there are 80 of them: 18,28,...808
    Now you know the sum of the numbers from 1 to 80 is 80*81/2. So, you have 10 times that sum, plus 80*8, including all the final digits.

    #3.
    a+5d = 2(a+2d)
    a+29d = 60
    solve for d.

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  2. 30

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