Question

已知等比數(shù)列{a_n}為遞增數(shù)列.若a₁>0,且2(a_n+a_n+2)=5a_n+1,則數(shù)列{a_n}的公比q=　　　　. 

Answer 1

2

∵數(shù)列{a_n}是遞增數(shù)列,且a₁>0,∴q>1,
∵2(a_n+a_n+2)=5a_n+1,
∴2a₁q^n-1+2a₁qⁿ⁺¹=5a₁qⁿ,
∴2q²-5q+2=0,
解得q=2或q=(舍去).