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:a₃·a₄=117,a₂+a₅=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) n= 4n-3 (2)c=-

【解析】(1)由得

解得或

∵公差d>0,∴a3=9,a4=13,∴d=4.

∴an=a3+(n-3)d=9+(n-3)·4=4n-3.

(2)Sn===2n2-n.

bn==.

∵{bn}是等差数列,

∴b1+b3=2b2.

∴+=2·,

∴2c2+c=0.

∵c≠0,∴c=-,经检验c=-符合题意.