What is the sum of a 10–term arithmetic sequence where the first term is 3 and the last term is 75?
To find the sum of an arithmetic sequence, you can use the formula for the sum of a finite arithmetic series:
Sum = (n/2)(first term + last term),
where n is the number of terms.
In this case, the first term (a) is 3, the last term (l) is 75, and the number of terms (n) is 10.
Plugging in the values into the formula, we get:
Sum = (10/2)(3 + 75)
First, evaluate the expression inside the parentheses:
Sum = (10/2)(78)
Next, simplify the expression by dividing 10 by 2:
Sum = 5(78)
Finally, multiply 5 by 78 to get the sum:
Sum = 390
Therefore, the sum of the 10-term arithmetic sequence is 390.