The following sum is a partial sum of an arithmetic sequence; use either formula for finding partial sums of arithmetic sequences to determine its value.
-9+1++561

16008

Step-by-step explanation:

Sum of an arithmetic sequence is:

S = (n/2) (2a₁ + (n−1) d)

or

S = (n/2) (a₁ + a)

To use either equation, we need to find the number of terms n.  We know the common difference d is 1 − (-9) = 10.  Using the definition of the nth term of an arithmetic sequence:

a = a₁ + (n−1) d

561 = -9 + (n−1) (10)

570 = 10n − 10

580 = 10n

n = 58

Using the first equation to find the sum:

S = (n/2) (2a₁ + (n−1) d)

S = (58/2) (2(-9) + (58−1) 10)

S = 29 (-18 + 570)

S = 16008

Using the second equation to find the sum:

S = (n/2) (a₁ + a)

S = (58/2) (-9 + 561)

S = 16008