posted by M.A. .
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?
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
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.
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
term(589) = 57 + (589-1)(2)
= 57 + 1176
= 1233 ... check!!
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
Just noticed that 'Writeacher' already gave you a detailed series of steps how to do this in Excel.
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!
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