∴( 1+4d)2=( 1+d)( 1+ 13d)，

d = 2(∵d > 0)∴an = 1+(n- 1)×2 = 2n- 1；

b2 = a2 = 3，a5=b3=9，

So the common ratio of geometric series {bn} is q=

b3

b2

=3,

∴bn=b2qn-2=3n- 1

(2)① Proof: √.

c 1

b 1

+

c2

b2

+…+

Communication network (short for Communicating Net)

billion

=an+ 1

When n≥2,

c 1

b 1

+

c2

b2

+…+

cn- 1

bn- 1

= Ann

Subtract two expressions to get.

Communication network (short for Communicating Net)

billion

=an+ 1-an=2(n≥2)。

② cn=2bn=2×3n- 1(n≥2) is obtained from ①.

When n= 1,

c 1

b 1

=a2, ∴c 1=3 does not satisfy the above formula.

∴c 1+c2+…+c20 14=3+2×3 1+2×32+…+2×320 13=3+

6-6×320 13

1-3

=3-3+320 14=320 14