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
e.g.
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!!

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....

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

http://www.jiskha.com/display.cgi?id=1244858200

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

25+10+15+15=

To determine the number of numbers in the given string, you can use a formula called the arithmetic sequence formula. The formula is:

n = (a + l) / 2,

where:
- n represents the number of terms in the sequence
- a represents the first term in the sequence
- l represents the last term in the sequence

In this case, the first term (a) is 57, and the last term (l) is 1233. Plugging these values into the formula, we get:

n = (57 + 1233) / 2 = 1290 / 2 = 645.

Therefore, there are 645 numbers in the given sequence.

Now, let's compare the two answers:
- Your friend calculated 588, which seems to be incorrect.
- You listed out all the numbers and found that there were 619, which is closer to the correct answer.

While listing out the numbers is a valid approach, it can be time-consuming and prone to mistakes. Using the arithmetic sequence formula is a quicker and more reliable method to determine the number of terms in a sequence. Therefore, it seems that your answer of 619 is more likely to be correct than your friend's answer of 588.