Proportional sequence, A3 and A9 are the two roots of equation x equal square + 3x + 1, A6=

Proportional sequence, A3 and A9 are the two roots of equation x equal square + 3x + 1, A6=

The equal ratio sequence, A3 and A9 are the two roots of the equation x equal square + 3x + 1
x1*x2=a3*a9=c/a=1
a6^2=a3*a9=1

If A3 = 3, A9 = 75, then A10 =?

a9/a3=q^6=25
So q = ± 5
So A10 = A9 * q = ± 75 * 5

It is known that in the equal ratio sequence {an} of which the common ratio is a real genus, A3 = 4, and A4, A5 + 4, A6 are equal difference sequence
Let the sum of the first n terms of the sequence {an} be Sn, and find the maximum value of (2An + 1) / Sn

2(A3*q²)=A3*q+A3*q³;
2q=1+q²;
(q-1)²=0;
q=1;\
An=4;
Sn=4+4+...+4=4n;
(2An+1)/Sn=9/4n;
When n = 1, the maximum value is 9 / 4;

If A3 * A5 * A7 * A9 * a11 = 32, what is ((A9) ^ 2) / 11

If A3, A5, a7, A9 and a11 are all positive integers
If and only if A3, A5, a7, A9 and a11 are all equal to 2, A3 * A5 * A7 * A9 * a11 = 32 holds
So ((A9) ^ 2) / 11 = 4 / 11