Question

按下列程序框圖運(yùn)算:

規(guī)定:程序運(yùn)行到“判斷結(jié)果是否大于244”為1次運(yùn)算.若x=5,則運(yùn)算進(jìn)行__________次才停止;若運(yùn)算進(jìn)行k(k∈N^*)次才停止,則x的取值范圍是__________.

Answer 1

答案：4  k=1時(shí),x∈(82,+∞),k≥2時(shí),x∈(1+3^5-k,1+3^6-k]

(1)第一次,5×3-2=13;

第二次,13×3-2=37;

第三次,37×3-2=109;

第四次,109×3-2=325＞244.

故四次才停止.

(2)k=1時(shí),3x-2＞244,x＞82.當(dāng)k≠1時(shí),

設(shè)每次結(jié)果構(gòu)成數(shù)列{a_k},則a₁=3x-2,a_k+1=3a_k-2.

∴a_k+1-1=3(a_k-1),數(shù)列{a_k-1}構(gòu)成以3x-3為首項(xiàng),3為公比的等比數(shù)列.

a_k-1=3(x-1)·3^k-1,a_k=3(x-1)·3^k-1+1,a_k＞244,∴3(x-1)·3^k-1＞243,

x-1＞243·()^k,x＞1+243·()^k=3^5-k+1.a_k-1≤244.

解得x≤3^6-k+1.∴x∈(3^5-k+1,3^6-k+1].