Equal ratio sequence a1 + A2 = 3, A3 + A4 = 6, find S8

Equal ratio sequence a1 + A2 = 3, A3 + A4 = 6, find S8

a3+a4=a1q^2+a2q^2=q^2(a1+a2)
6=3q^2
q^2=2
a5+a6
=q^2(a3+a4)
=2*6
=12
a7+a8
=q^2(a5+a6)
=2*12
=24
s8=a1+a2+a3+a4+a5+a6+a7+a8
=3+6+12+24
=45

Equal ratio sequence: if A2 + A1 = 2, A3 + A4 = 8, then S8 =?

a2=a1*q
So A2 + A1 = A1 * (1 + Q) = 2
Similarly, A3 + A4 = A1 * (Q-square + q-cube) = A1 * Q-square * (1 + Q) = 8
So there is
a1=2/3
q=2
So S8 = [(2 / 3) (1-2 ^ 8)] / (1-2)
So S8 = 85

In {an}, if q = 2, s99 = 77, then A3 + A6 + +a99=______ ．

Because {an} is an equal ratio sequence with a common ratio of 2, let A3 + A6 + A9 + +A99 = x, then a1 + A4 + A7 + +a97=x4，a2+a5+a6+… +a98=x2．S99=77=（a1+a4+a7+… +a97）+（a2+a5+a6+… +a98）+（a3+a6+a9+… +a99）=x+x2+x4=74x，∴a3+a6+a9+… A99 = 44, so the answer is: 44

In the equal ratio sequence {an}, if the common ratio q = 2 and the sum of the first 99 terms s99 = 30, then A3 + A6 + A9 + a99=______ ．

Because {an} is an equal ratio sequence with a common ratio of 2, let A3 + A6 + A9 + +A99 = x, then a1 + A4 + A7 + +a97=x4a2+a5+a8+… +a98=x2S99=30=（a1+a4+a7+… +a97）+（a2+a5+a6+… +a98）+（a3+a6+a9+… +a99）=x+x2+x4∴a3+a6+a9+… A99 = 1207, so the answer is: 1207

In the equal ratio sequence {an}, if the common ratio q = 2 and the sum of the first 99 terms s99 = 30, then A3 + A6 + A9 + a99=______ ．

Because {an} is an equal ratio sequence with a common ratio of 2, let A3 + A6 + A9 + +A99 = x, then a1 + A4 + A7 + +a97=x4a2+a5+a8+… +a98=x2S99=30=（a1+a4+a7+… +a97）+（a2+a5+a6+… +a98）+（a3+a6+a9+… +a99）=x+x2+x4∴a3+a6+a9+… A99 = 1207, so the answer is: 1207