Question

等差数列习题【求解析】1、在等差数列{a(n)}中,已知a(1)=1/3,a（2）+a（5）=4,a（n）=33,求n.

Answer 1

(1)

a2 = a1 + d

a5 = a1 + 4d

a2 + a5 = 2a1 + 5d = 4

5d = 4 - 2a1 = 10/3

d = 2/3

an = a1 + (n - 1)d

= 1/3 + 2(n - 1)/3

= (2n - 1)/3 = 33

2n - 1 = 99

n = 50

(2)

a,x ,b ,2x .依次成等差数列

b=(2X+X)/2

=3/2 X

同理：X=(a+b)/2

2X=a+b

a=2X-b

因为b=3/2 X

所以a=1/2 X

所以b:a=3:1

(3)

最大数是7*56+105

最小数是7*28+105

所以,共有 56-28+1=29项