3) En la siguiente sucesión: 5; 9; 13; 17; ...; 257. ¿Qué posición ocupa el último término?

33rd term

Step-by-step explanation:

To get the number of terms of the sequence, we will use the sum of nth term of the sequence formula;

Sn = n/2(a+l)

Tn = a + (n-1)d

a = 5

d = 9-5 = 13-9 = 4

Tn = 5 + (n-1)4

Tn = 5 + 4n-4

Tn = 4n+1

Sn = n/2(5+257)

Sn = 262n/2

Sn = 131n

Sn-1 = 131(n-1)

Sn-1 = 131n-131

Since Tn = Sn - Sn-1

4n + 1 = 131n - 131n + 131

4n + 1 = 131

4n = 131 - 1

4n = 130

n = 130/4

n = 32.5

n ≈ 33

Since n = 32.5 Hence257 occupies the 33rd term in the sequence

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

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step-by-step explanation: