Question

高中数学数列问题求解

高中数学数列问题求解如图，求过程

Answer 1

如图

追答

Answer 2

Answer 3

a1=8, a4=2
a(n+2)-2a(n+1) +an =0
a(n+2)-a(n+1) = a(n+1) -an
=>{a(n+1) -an } 是等比数列， 公比 =1
a4-a3 =1 (1)
a3-a2 =1 (2)
a2 -a1 =1 (3)
(1)+(2)
a4-a2 =2
2-a2=2
a2 = 0
a(n+1) -an =a2 -a1
=-8
=> {an} 是等差数列，公差=-8
an= -8(n-1) + a1
= -8(n-1) + 8
=-8n +16
an >0
-8n+16 >0
n=1, S1 =a1 = 8
n=2 , S2 = a1+a2 =8
n>2
Sn
=|a1|+|a2|+...+|an|
=8 -( a3+a4+...+an)
=8 -(1/2)(a3+an)(n-2)
=8-(1/2)(n-2)(-8 -8n +16)
=8-(1/2)(n-2)(8 -8n)
=8+ 2(n-2)(n-1)
=2n^2 -6n +12