An is the arithmetic sequence, A3 + A8 = 16, A6 = 7 to find the tolerance D

An is the arithmetic sequence, A3 + A8 = 16, A6 = 7 to find the tolerance D


a3+a8=a6-3d+a6+d=7+7-d=16,
d=-2



In the known arithmetic sequence {an}, A6 = 5, and A3 + A8 = 5, find: (1) A1 and tolerance D; (2) the sum of the first 18 terms


(1) ∵ A6 = 5, and A3 + A8 = 5, ∵ A5 + 5 = 5, that is, A5 = 0, ∵ d = a6-a5 = 5, then A1 = a5-4d = 0-4 × 5 = - 20; (2) S18 = − 20 × 18 + 18 × 17 × 52 = 405



Given that A1 = 12, A6 = 27, find D


Is it an arithmetic sequence
a6=a1+5d
27=12+5d
d=3