feliciaamalapane feliciaamalapane
  • 13-08-2022
  • Mathematics
contestada

What is the formula of the sequence 3, 6, 10, 15, 21?​

Respuesta :

fireopal666
fireopal666 fireopal666
  • 13-08-2022

Answer:

Tn=12n(n+1)

Step-by-step explanation:

Explanation:

These are the triangular numbers - each term in the sequence being the sum of the first n positive integers:

T1=1=1

T2=3=1+2

T3=6=1+2+3

etc.

Notice that:

2Tn=(0)+1+(0)+2+...+(n−1)+(0)+n

2Tn+(0)+n+(n−1)+...+(0)+2+(0)+1

2Tn=(n+1)+(n+1)+...+(n+1)+(n+1)

2Tn=n(n+1)

So:

Tn=12n(n+1)

Answer Link
seokjinnie777
seokjinnie777 seokjinnie777
  • 13-08-2022

Answer:

[tex]a_{n} = \frac{n^{2}}{2} +\frac{3n}{2} +1[/tex]

hope this helps! <3

Answer Link

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