What is the sum of a 12–term arithmetic sequence where the last term is 13 and the common difference is –10?
To find the sum of an arithmetic sequence, you can use the formula:
sum = (number of terms / 2) * (first term + last term)
In this case, the number of terms is 12, the first term is not given directly, and the last term is 13.
To find the first term of the arithmetic sequence, we need to use the formula:
last term = first term + (number of terms - 1) * common difference
Given that the last term is 13 and the common difference is -10, we can substitute these values into the formula to solve for the first term:
13 = first term + (12 - 1) * (-10)
13 = first term + 11 * -10
13 = first term - 110
first term = 13 + 110
first term = 123
Now that we have determined the first term, we can substitute the values into the formula for the sum:
sum = (12 / 2) * (123 + 13)
sum = 6 * 136
sum = 816
Therefore, the sum of the 12-term arithmetic sequence is 816.