等差數(shù)列(2)復(fù)習(xí)：1.已知數(shù)列{an}的a3=15,a15=3,則a18=_______.3.已知函數(shù)f(x)滿足:若f(1)=2,則f(100)=________.4.一種公差為整數(shù)的等差數(shù)列的首項(xiàng)是-25,從第10項(xiàng)起,開(kāi)始為正數(shù),則公差d=______.2.已知數(shù)列{an}的前3項(xiàng)依次是x-1,x+1,2x+3,則這個(gè)數(shù)列的通項(xiàng)是__________.5.若數(shù)列a,x1,x2,b與數(shù)列a,y1,y2y,y3,b均是等差數(shù)列(a≠b),則6、判斷下列數(shù)列與否是等差數(shù)列.討論:1.已知數(shù)列{an}:a1,a2,a3,…,an,…是等差數(shù)列,(1)數(shù)列:an,an-1,…,a2,a1還是等差數(shù)列嗎?(2)數(shù)列a2,a4,a6,…,a2n,…是等差數(shù)列嗎?(3)數(shù)列2a1,2a2,2a3,…,2an,…是等差數(shù)列嗎?(4)數(shù)列ka1+b,ka2+b,ka3+b,…,kan+b,…是等差數(shù)列嗎?2.在等差數(shù)列{an}中,(1)a1+a7=a3+a5成立嗎?(2)若m+n=p+q,有am+an=ap+aq成立嗎?(m,n,p,q∈N+)(3)若m+n=2p,有am+an=2ap成立嗎?(m,n,p∈N+)1.在等差數(shù)列{an}中,例題:(1)a3+a11=a6+a()=()a7(2)若a5+a13=40,a8+a9+a10=___________(3)若a4+a6+a8+a10+a12=120,則(4)若a3+a7-a10=8,a11-a4=4,則a7=_____(5)若a2+a3+a4+a5=34,a2·a5=52,則公差d=_____2.(1)已知a+b+c=15,且b是a,c的等差中項(xiàng),成等差數(shù)列,求a,b,c的值.(2)已知等差數(shù)列的四個(gè)數(shù)之和為26,第二個(gè)數(shù)與第三個(gè)數(shù)的積是40,求這四個(gè)數(shù).3.(1)已知a,b,c的倒數(shù)成等差數(shù)列,求證:也成等差數(shù)列.(2)已知a,b,c成等差數(shù)列,問(wèn):與否成等差數(shù)列?4.(1)已知數(shù)列{an}的通項(xiàng)求證:數(shù)列{an}是等差數(shù)列.(2)已知數(shù)列{an}的前n項(xiàng)的和問(wèn):數(shù)列{an}是等差數(shù)列嗎?拓展延伸:1.已知等差數(shù)列{an}中,a1=2,a2=3,若在每相鄰兩項(xiàng)之間插入三個(gè)數(shù),使它和原數(shù)列的數(shù)構(gòu)成一種新的等差數(shù)列,求:(1)原數(shù)列中的第12項(xiàng)是新數(shù)列中的第幾項(xiàng)?(2)新數(shù)列中的第29項(xiàng)是原數(shù)列中的第幾項(xiàng)?2.已知兩個(gè)等差數(shù)列5,8,11,…和3,7,11,…都有100項(xiàng),問(wèn)它們共有多少相似的項(xiàng)?并寫(xiě)出由全部共同的項(xiàng)按從小到大排列所構(gòu)成的數(shù)列的通項(xiàng).3.已知數(shù)列{an}滿足:a1=4,,設(shè)(1)求證數(shù)列{bn}是等差數(shù)列;(2)求數(shù)列{an}的通項(xiàng).4.如圖,在XOY平面上有一系列點(diǎn)對(duì)于每一種正整數(shù)n,點(diǎn)Pn都在y=x2(x≥0)的圖象上,以點(diǎn)Pn為圓心的⊙Pn與x軸都相切,且⊙Pn與⊙Pn+1又彼此相切,若x1=1,且xn+1<xn,(1)求證:數(shù)列是等差數(shù)列.(2)求第10個(gè)圓的半徑.PnPn+1Oyxy=x2(x≥0)課堂小結(jié)1.等差數(shù)列的概念及通項(xiàng)公式.(1)an－an-1=d(n≥2)或an+1－an=d(2)an=a1+(n－1)d.

an=am+(n－m)d.

2.等差數(shù)列的性質(zhì):(1)若m+n=p+q,則am+an=ap+aq(m,n,p,q∈N+)(2)若m+n=2p,則am+an=2ap(m,n,p∈N+)(4)若{an},{bn}為等差數(shù)列,則數(shù)列{kan+c},{an+bn}仍成等差數(shù)列.(3)am+k,am+2k,am+3k,…,仍成等差數(shù)列.1.已知數(shù)列{an}中,求a18.2.已知關(guān)于x的方程有兩個(gè)相等的實(shí)數(shù)根,求證:成等差數(shù)列.3.已知數(shù)列{an}的前n項(xiàng)的和,