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
Accepted Solution
A:
Answer:16008Step-by-step explanation:Sum of an arithmetic sequence is:S = (n/2) (2a₁ + (n−1) d)orS = (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) d561 = -9 + (n−1) (10)570 = 10n − 10580 = 10nn = 58Using 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 = 16008Using the second equation to find the sum:S = (n/2) (a₁ + a)S = (58/2) (-9 + 561)S = 16008