在等比数列An中，公比为0.5，且a3+a6+a9+......+a99=60求a1+a2+a3+a4+......+a99的值

A3=0.5×A2 A6=0.5×A5 A9=0.5×A8 ……
A2=0.5×A1 A5=0.5×A4 A8=0.5×A7 ……
A2+A5+A8+……+A98=60÷0.5=120
A1+A4+A7+……+A97=120÷0.5=240
A1+A2+A3+A4+……+A99=60+120+240=420

a(n) = a/2^(n-1), n = 1,2,...

60 = a(3) + a(6) + a(9) + ... + a(99) = a/2^2 + a/2^5 + a/2^8 + ... + a/2^98 = a/4[1 + 1/2^3 + (1/2^3)^2 + ... + (1/2^3)^32]
= a/4[1 - (1/2^3)^33]/[1 - 1/2^3] = a[1 - 1/2^99]/[4 - 1/2],

a(1) + a(2) + ... + a(99) = a + a/2 + ... + a/2^98
= a[1 + 1/2 + ... + (1/2)^(98)]
= a[1 - (1/2)^99]/[1 - 1/2]
= 60*[4-1/2]/[1-1/2]

= 60*[8-1]
= 420