Question

what is a rule of next three terms of 6, 10, 15, 21, ....., ......, .....

Answer 1

b(k) means k th term
b(k+1)=b(k)+3+k

Answer 2

written as a recursive :
t(1) = 6
t(n) = t(n-1) + k+1, where k >1

as a function of n,
double the terms: 12, 20, 30, 42 ...
12 = 3*4
20 = 4*5
30 = 5*6
42 = 6*7

looks like
t(n) = (n+2)(n+3)/2 <--- remember we doubled