Final answer:
The sum of the first 70 terms of the arithmetic sequence -20, -28, -36, -44 is -20720, calculated using the formula for the sum of an arithmetic sequence.
Step-by-step explanation:
To find the sum of the first 70 terms of the arithmetic sequence -20, -28, -36, -44, we need to use the formula for the sum of an arithmetic sequence, which is:
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, and a_n is the nth term. The sequence has a common difference d, which we find by subtracting any term from the term that follows it.
For this sequence, the first term a_1 is -20 and the common difference d is -8 (since -28 - (-20) = -8).
To find the 70th term a_70, we use the formula:
a_n = a_1 + (n - 1)d
Let's calculate a_70:
a_70 = -20 + (70 - 1)(-8)
a_70 = -20 - 69 * 8
a_70 = -20 - 552
a_70 = -572
Now we can find the sum S_70:
S_70 = 70/2 * (-20 + (-572))
S_70 = 35 * (-592)
S_70 = -20720
The sum of the first 70 terms of the arithmetic sequence is -20720.