Question

已知{a n }为等差数列，S n 为其前n项和，若a 1 = 1 2 ，S 2 =a 3 ，则a 2 =______，S n =___

已知{a n }为等差数列，S n 为其前n项和，若a 1 = 1 2 ，S 2 =a 3 ，则a 2 =______，S n =______．

Answer 1

根据{a n }为等差数列，S 2 =a 1 +a 2 =a 3 = 1 2 +a 2 ； ∴d=a 3 -a 2 = 1 2 ∴a 2 = 1 2 + 1 2 =1 S n = 1 2 n+ n(n-1) 2 × 1 2 = 1 4 n(n+1) 故答案为：1， 1 4 n(n+1)