Question

等差数列｛an｝中，已知a1=1/3,a2+a5=4,an=33(1)求n的值(2)求a8+a9+

等差数列｛an｝中，已知a1=1/3,a2+a5=4,an=33(1)求n的值(2)求a8+a9+a10+a11+a12的值(3)求s50的值

Answer 1

由题意 a2+a5 = (a1+d)+(a1+4d) = 2a1+5d = 2/3 +5d = 4
所以 d = 2/3
an = a1+(n-1)d = 1/3 +(2/3)(n-1) = (2/3)n -1/3 = 33
所以 n = 50
a8+a9+a10+a11+a12 = (a10-2d)+(a10-d)+a10+(a10+d)+(a10+2d) = 5a10 = 5*(a1+9d) = 95/3
S50 = (a1+a50)*50/2 = (1/3 +33)*25 = 2500/3

Answer 2

（1）a2+a5=a1+a6 4=（1/3）+a6 a6=11/3=a1+（6-1）d
得d=2/3 an=33=a1+（n-1）d=1/3+（n-1）*2/3 得n=50
（2） a10=19/3 a8+a9+a10+a11+a12=5a10=5*19/3=95/3
（3）a50=33 S50=50（a1+a50）*1/2=2500/3