In the equal ratio sequence {an} with known common ratio 2, A2 + A5 + A8 + a11 + A14 + A17 + A20 = 13, then what is the sequence A1? (find the whole process)

In the equal ratio sequence {an} with known common ratio 2, A2 + A5 + A8 + a11 + A14 + A17 + A20 = 13, then what is the sequence A1? (find the whole process)


If {an} is an equal ratio sequence and the common ratio is 2, then A2, A5, A8, a11, A14, A17, A20 also constitute an equal ratio sequence
The first item is A2, the common ratio is 8, and the number of items is 7
Then A2 + A5 + A8 + a11 + A14 + A17 + A20
=a2(1-8^7)/(1-8)=13
That is, A2 = 91 / (8 ^ 7-1)
And A1 * q = A2,
That is A1 * 2 = 91 / (8 ^ 7-1)
Then A1 = 91 / 2 (8 ^ 7-1)



Let the sum of the first n terms of the equal ratio sequence < an > be Sn, if A1 = 1, S6 = 4S3, then A4 =?


S6=1-q^6/1-q=4*1-q^3/1-q
That is, (1-Q ^ 3) (1 + Q ^ 3) = 4 (1-Q ^ 3)
So 1 + Q ^ 3 = 4 is Q ^ 3 = 3
So A4 = a1q ^ 3 = 1 * 3 = 3