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laiz [17]
2 years ago
5

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

Mathematics
2 answers:
poizon [28]2 years ago
4 0

Answer:

a_{n}  = \frac{n^{2}}{2} +\frac{3n}{2} +1

hope this helps! <3

AleksAgata [21]2 years ago
3 0

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)

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