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