what is the sum of the odd numbers 1-2009
number of terms ---- n
a=1
term(n) = a + (n-1)d
2009 = 1 + (n-1)2
2009 = 1 + 2n - 2
2n = 2010
n = 1005
sum = (1005/2) (1 + 2009) = 1010025
To find the sum of the odd numbers from 1 to 2009, you can use a formula that calculates the sum of an arithmetic series. However, since 2009 is an odd number itself, the last odd number in the sequence will be 2009.
To find the sum, we need to calculate the number of terms in the sequence and then use the formula for the sum of an arithmetic series.
The first step is to determine the number of terms in the sequence. We can do this by subtracting the first odd number, 1, from the last odd number, 2009, and then dividing the result by 2 and adding 1 since the common difference is 2.
Number of terms = ((2009 - 1) / 2) + 1
Next, we can use the formula for the sum of an arithmetic series:
Sum = (number of terms / 2) * (first term + last term)
In this case, the first term is 1, and the last term is 2009.
Now, let's calculate the sum:
Number of terms = ((2009 - 1) / 2) + 1 = (2008 / 2) + 1 = 1004 + 1 = 1005
Sum = (number of terms / 2) * (first term + last term) = (1005 / 2) * (1 + 2009) = 502.5 * 2010 = 1,011,050
Therefore, the sum of the odd numbers from 1 to 2009 is 1,011,050.