Question

已知公差大于零的等差数列{a n }的前n项和为S n ,且满足:a 3 ·a 4 =117,a 2 +a 5 =22.(1)求数列{a n }的

已知公差大于零的等差数列{a n }的前n项和为S n ,且满足:a 3 ·a 4 =117,a 2 +a 5 =22.(1)求数列{a n }的通项公式a n .(2)若数列{b n }是等差数列,且b n = ,求非零常数c.

Answer 1

(1) n = 4n-3          (2)c=-

(1)由 得 解得 或 ∵公差d>0,∴a 3 =9,a 4 =13,∴d=4. ∴a n =a 3 +(n-3)d=9+(n-3)·4=4n-3. (2)S n = = =2n 2 -n. b n = = . ∵{b n }是等差数列, ∴b 1 +b 3 =2b 2 . ∴ + =2· , ∴2c 2 +c=0. ∵c≠0,∴c=- ,经检验c=- 符合题意.