Question

n 1 2 3 4 5 6 ... n ... 20
f(n) 1 3 6 10 15 21...___...____


find the n term .
thanks.

Answer 1

f(n) = n(n+1)/2

The numbers produced by f(n) are called the triangular numbers.
Have you ever noticed the number of balls in setting up the triangle in billiards?
sum of balls in first row : 1
sum of balls after 2 rows: 3
sum of balls after 3 rows : 6
sum of balls after 4 rows: 10
etc.
so f(20) = 20(21)/2 = 210