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

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