Question

In the 20th row of following triangle
1
2 3
4 5 6
7 8 9 10
...........................
..........................

Answer 1

what is its sum?

Answer 2

If you look property, consider the 1st column only. the terms are
1,2,4,7 the next term will be 11 and then 16 and so on...
See you need to have a formula for a general term of this series

Answer 3

*sequence

Answer 4

ok, after minor calculations you will find that the general term of the sequence of the 1st column is t_n=(n^2-n+2)/2
so t_20=191

Answer 5

now the 20th row will have entries 191,192,...,210

Answer 6

so the sum will be 191+192+...+210=(190+1)+(190+2)+(190+3)+...+(190+20)=20*190+(1+2+3+...+20)=20*190+(20)*(20+1)/2=4010

Answer 7

@Ambuj