Answer:
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
