Question

已知公差大于零的等差數(shù)列{a_n}的前n項和為S_n,且滿足:a₃·a₄=117,a₂+a₅=22.
(1)求數(shù)列{a_n}的通項公式a_n.
(2)若數(shù)列{b_n}是等差數(shù)列,且b_n=,求非零常數(shù)c.

Answer 1

(1) _n= 4n-3          (2)c=-

(1)由得
解得或
∵公差d>0,∴a₃=9,a₄=13,∴d=4.
∴a_n=a₃+(n-3)d=9+(n-3)·4=4n-3.
(2)S_n===2n²-n.
b_n==.
∵{b_n}是等差數(shù)列,
∴b₁+b₃=2b₂.
∴+=2·,
∴2c²+c=0.
∵c≠0,∴c=-,經(jīng)檢驗c=-符合題意.