Question

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

Answer 1

Tn=12n(n+1)

Step-by-step explanation:

Step-by-step 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 2

`a_(n) = (n^(2))/(2) +(3n)/(2) +1`

hope this helps! <3