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Math..number string

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How many numbers are in the string
57, 59, 61, 63,...1233?

My friend calculated 588.
I am too concrete in my thinking and did it the hard way, listing all of the numbers on an Excel sheet and found that there were 619 numbers. Who is correct?
And how is this calculated?

  • Math..number string -

    You have an "arithmetice sequence"
    with the first number as 57 and a common difference of 2

    the general term of any arithmetic sequence is given by
    term(n) = a + (n-1)d, were n is the term number,
    a is the first term, and
    d is the common difference

    so we have 1233 = 57 + (n-1)(2)
    1233 = 57 + 2n - 2
    1178 = 2n
    n = 589

    so there are 589 terms

  • Math..number string -

    I have actually printed out all of the numbers "57, 59, 61,63, all the way to 1233". There are 619 numbers. I double checked for errors that all of the numbers were correct. There are actually 619 numbers, for real. The mathematical formula you used does not match with the actual print-out of the real numbers. Please explain.

    Can you run the real numbers as a double-check for your formula and see what shows up on a list of counted numbers? The formula does not appear to agree with reality.

  • Math..number string -

    sorry, this is a well-known formula and is correct.
    There is no need to "run the the real numbers as a double-check"

    let's check some of the numbers
    term(4) = 57 + (4-1)(2)
    = 57 + 6 = 63 ...check!

    term(612) = 57 + (612-1)(2) = 1278
    This was you answer, but obviously doesn't verify

    my answer:
    term(589) = 57 + (589-1)(2)
    = 57 + 1176
    = 1233 ... check!!

  • Math..number string -

    here is a quick way to verify my answer
    and to show your list has an error in it.

    go to Excel
    enter 57 into A1
    in A2 enter the formula "= A1 + 2"

    highlight columns A down to your 612
    and use the 'copy down' to enter the formula in all those cells

    now look in A589
    Well, well....

  • Math..number string -

    Just noticed that 'Writeacher' already gave you a detailed series of steps how to do this in Excel.

  • Math..number string -

    In doing the Excel list, my column A589 has the number 1177 listed. In checking the list of real numbers again, I have found another major error. Thank you so much for your patient help in working with this mathematically challenged individual.But at least I am learning!

  • Math..number string -

    check that in your Excel list such values as A1 = 57 ,A2 = 59 etc are correct

    if A4 = 63 but A589 is not equal to 1233 there has to be something wrong with your cell formula, or God forbid, your EXcel program

  • Math..number string -


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