Write an
explicit formula for An, the nth term of the sequence 20, 30, 40,

= 10n + 10

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence

d = 30 - 20 = 40 - 30 = 10

This indicates the sequence is arithmetic with explicit formula

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 20 and d = 10, thus

= 10 + 10(n - 1) = 10 + 10n - 10 = 10n + 10

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