Question

高一 数学 已知数列{an}是等差数列 请详细解答,谢谢! (24 20:19:28)

1、已知数列{an}是等差数列，若a4 + a7 + a10 =17，a4 + a5 + a6 +…+ a12 + a13 + a14 =77，且ak =13，则k=?

Answer 1

a4 + a7 + a10 =17=3a7(a4+a10=2a7)
所以a7=17/3
a4+a14=a5+a13=a6+a12=a7+a11=a8+a10=2a9
所以a4 + a5 + a6 +…+ a12 + a13 + a14 =
11a9=77
所以a9=7
a9-a7=2d=7-17/3=4/3
d=2/3
a7=a1+6d=a1+8=17/3,得a1=-7/3
所以ak=a1+(k-1)d=-7/3+(k-1)4/3=-11/3+4k/3
令-11/3+4k/3=13
得k=12.5 (不晓得你题抄对没，不是整数)

Answer 2

由a4 + a7 + a10 =17得，a7=17/3
由a4 + a5 + a6 +…+ a12 + a13 + a14 =77得，a9=7
所以公差d=2/3
ak=a9+2/3*(k-9)=13
所以7+2/3*(k-9)=13
k=18

Answer 3

a4+a7+a10=17 => 3a7=17 => a7=17/3
a4 + a5 + a6 +…+ a12 + a13 + a14 =77 => 11a9=77 => a9=7
d=(a9-a7)/2=2/3
17/3+(k-7)*2/3=13 => k=18

Answer 4

K=21