The sum of the first 10 terms of a geometric sequence is 4-2^(-8). If the common ratio is 1/2, find the first term of the sequence. Use this to determine the 11th term of the sequence.

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0

=

x=0.8898305 is the answer to that equation