Q. 105.0( 4 Votes )

# <img width="180"

Answer :

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**

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