Write the next two lines of the pattern above. Calculate the first and last terms of the 20th line.

The first terms of each line are 4,7,13,22…

The difference between each consecutive term is

7-4 = 3

13-7 = 6

22-13 = 9

i.e. 3,6,9… in AP

For 4^th line,

First term = 22 + 12 = 34 , d = 3

For 5^th line

First term = 34 + 15 = 49 , d = 3

Also from observation, nth line has n terms

Hence, 4^th line

34,37,40,43

And 5^th line

49,52,55,58,61

The sequence of common difference is

The difference between the first terms of each line forms an AP which is

3,6,9…

For first term of 20^th line, sum of 19 terms of above sequence to be added to first term of first line.

Sum of 19 terms =

= 570

For 20^th line,

First term = 4 + 570 = 574

It has 20 terms

Last term = 574 + 19×3 = 574 + 57 = 631