1 2 3 4 .... 1002 what is the sum of the sequence
Mathematics · High School · Thu Feb 04 2021
Answered on
The sequence given is an arithmetic sequence (or arithmetic progression) starting at 1 and ending at 1002, with a common difference of 1 between each term (since each number in the sequence is 1 more than the previous number).
The sum of an arithmetic sequence can be found using the formula:
S_n = n/2 * (a_1 + a_n)
where: - S_n is the sum of the first n terms. - n is the number of terms. - a_1 is the first term. - a_n is the nth term.
In this case: - a_1 = 1 (the first term) - a_n = 1002 (the last term)
The number of terms (n) can be found by subtracting the first term from the last term, dividing by the common difference, and adding 1.
n = (1002 - 1)/1 + 1 = 1002
Now, we can plug the values into the sum formula:
S_n = 1002/2 * (1 + 1002) S_n = 501 * 1003 S_n = 502503
So, the sum of the sequence from 1 to 1002 is 502,503.