Question

数列中，a3十a5十a7十a9十a11=100则3a9一a13=

Answer 1

假设a0为首项,d为公差，侧an= a0 + nd
a3+a5+a7+a9+a11=100
==>5a0+(3+5+7+9+11)d = 100
==>5a0+35d = 100
==>a0 + 7d = 20

3a9 - a13
= 3(a0 + 9d) - (a0+13d)
= 2a0+14d
= 2(a0 + 7d)
= 40

追问

a2十a3十a4十a5=34，a2乘a5=52，求公差d，己知a13=12

追答

4a + 14d = 34
==>2a + 7d = 17

(a+2d)*(a+5d)=52
==>a^2 + 7ad + 10d^2 = 52

a13=12
==>a + 13d = 12

2a + 7d = 17
a + 13d = 12
==> d = 7/19
我咋感觉多了个条件？
两个未知数，两个方程，足够了。怎么给出了三个条件，即三个方程？

a^2 + 7ad + 10d^2 = 52

Answer 2

什么数列说清楚，随机数列无唯一解

追问

等差
不好意思

追答

因为是等差数列，所以a3+a11=a5+a9=2a7，5a7=100， a7=20
a9=a7+2d,a13=a7+6d，3a9-a13=3(a7+2d)-(a7+6d)=2a7=2*20=40

追问

thank you
a2十a3十a4十a5=34，a2乘a5=52，求公差d，己知a13=12
等差数列