AceClove AceClove
  • 25-07-2022
  • Mathematics
contestada

Determine the explicit formula for the sequence 4, 7, 14, 25

Respuesta :

parsahosseinal14 parsahosseinal14
  • 25-07-2022

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]

Answer Link

Otras preguntas

What is 6000 minus 3672?
Help I am going to die
A revenue should be recorded when A. it’s earned. C. the invoice is sent to the customer. D. None of the above
State one reason for rapid population growth in megacities. Explain one reason why this growth is concentrated at the rural-urban fringe.
How does applying oil to a bicycle help the bicycle to work better?
In what two way can gender inequality/unequal power relations contribute to the spread of HIV infections?
i need a quotes for health class please help
24:40 in equivalent ratio 12:? ?:80 what is the answer then i dont get it
What are the major structures of the bone and their respective subcategories?
What important step did Prime Minister William Pitt take to win the war in North America?