The first term of a geometric sequence is 12 and the sum of the first two terms is 35. Work out the sum of the first 10 terms of the sequence.

Give your answer as a decimal correct to 3 significant figures.

8745.530

Step-by-step explanation:

a₁ = 12

S₂ = 12*(1-r²)/(1-r) = 35

12*(1+r)*(1-r)/(1-r) = 12(1+r) = 35

12r = 23           r = 23/12

S₁₀ = 12*(1-(23/12)¹⁰)/(1-(23/12)

     = 8745.530

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.