In this paper, we show that a ringRsatisfies unit 1-stable range if and only ifa1R+ ⋯ +amR=dRwithm≥ 2,a1, ⋯amϵRimplies that there existu1, ⋯umϵU(R) such thata1u1+⋯+amum= d and an exchange ringRhas stable range one if and only ifa1R+⋯+amR=dRwithm≥ 2,a1,⋯,amϵRimplies that there exist unit-regularw1,⋯,wmϵRsuch thata1w1+⋯+amwm= d. Also we show that an exchange ringRsatisfies then-stable range condition if and only ifa(nR)+bR=dRwithaϵRn,b,dϵRimplies that there exist unimodular regularwϵnRand:yϵRsuch thataw+by = d.