Respuesta :

Step-by-step explanation:

You already know that we use tn=an²+bn+c for these kinds of sequences:

4, 7, 14, 25, ...

  1. 7–4=3
  2. 14–7=7

now

7–3=4

So 2a=4===> a=2

[tex] a_{1} = 4 = = > n = 1 \\ 4 = 2 \times {1}^{2} + b + c = = = = > \\ b + c = 2[/tex]

[tex] a_{2} = 7 = = > n = 2 = = = > \\ 7 = 2 \times {2}^{2} + 2 \times b + c = = = > \\ - 1 = 2b + c[/tex]

  1. b+c=2
  2. 2b+c=–1

b=–3, c=5

So the final result is:

[tex] t_{n} = 2 {n}^{2} - 3n + 5[/tex]