{an} is an equal ratio sequence. If A8 is equal to 2 than A4 and S4 = 4, then the value of S8 is equal to 4 Specific steps and methods should be taken

{an} is an equal ratio sequence. If A8 is equal to 2 than A4 and S4 = 4, then the value of S8 is equal to 4 Specific steps and methods should be taken

∵a8/a4=(a1q^7)/(a1q^3)=q^4=2
∴S4=[a1(1-q^4)]/(1-q)=-a1/(1-q)=4
∴a1=-4(1-q)
S8=[a1(1-q^8)]/(1-q) = {-4(1-q)[1-(q^4)^2]}/(1-q) = -4(1-2^2) = 12

Let {an} be an equal ratio sequence, if A8 / A4 = 2, S4 = 4, then the value of S8 is equal to

Let S8 = t
From A8 / A4 = 2
We know that Q ^ 4 = 2 and Q ≠ 1
And S4 = A1 (1-Q ^ 4) / (1-Q) = 4
S8=a1（1-q^8)/(1-q)=t
The above two formulas are compared
（1-q^4)/(1-q^8)=4/t
That is, (1-Q ^ 4) / (1-Q ^ 4) (1 + Q ^ 4) = 4 / T
That is 1 / (1 + Q ^ 4) = 4 / T
That is 1 / (1 + 2) = 4 / T
That is, 1 / 3 = 4 / T
The solution is t = 12
So S8 = 12

If A8 / A4 = 2, S4 = 4, then S8 is equal to
Detailed
High 2 math
Be in a hurry

d^4=2
S8=S4+S4d^4=12

If A8 / A4 = 2, S4 = 4, then A8 =?

Wrong. We should ask for S8
a8/a4=q^4=2
S4=a1(1-q^4)/(1-q)=4
a1/(1-q)=-4
So S8 = A1 (1-Q ^ 8) / (1-Q)
=-4*(1-2²)
=12