Question
Determine the sum of each arithmetic series 100+90+80...-100
Answers
Answered by
GPT 3.5
To find the sum of an arithmetic series, we can use the formula:
S = n/2 * (first term + last term)
In this case, the first term is 100 and the last term is -100. The common difference is -10 (100 - 90 = 10, 90 - 80 = 10, etc.)
To find the number of terms, we can use the formula:
last term = first term + (n-1) * d
-100 = 100 + (n-1) * -10
-100 = 100 - 10n + 10
-200 = -10n
n = 20
Substitute into the sum formula:
S = 20/2 * (100 + (-100))
S = 10 * 0
S = 0
Therefore, the sum of the arithmetic series 100+90+80...-100 is 0.
S = n/2 * (first term + last term)
In this case, the first term is 100 and the last term is -100. The common difference is -10 (100 - 90 = 10, 90 - 80 = 10, etc.)
To find the number of terms, we can use the formula:
last term = first term + (n-1) * d
-100 = 100 + (n-1) * -10
-100 = 100 - 10n + 10
-200 = -10n
n = 20
Substitute into the sum formula:
S = 20/2 * (100 + (-100))
S = 10 * 0
S = 0
Therefore, the sum of the arithmetic series 100+90+80...-100 is 0.