Write the next two lines of the pattern above. Calculate the first and

1.	Write the next two lines of the pattern above. Calculate the first and last terms of the 20th line.
Answer» 4, 7, 13, 22, 34, 49,……. (4, 4 + 3, 7 + 6, 13 + 9, 22 + 12, 34 + 15), Generally it written as 4 + 3(1 + 2 + 3 + ………..) First term in the fifth row = 4 + 3(1 + 2 + 3 + 4) = 4 + 30 = 34 First term in the sixth row = 4 + 3(1 + 2 + 3 + 4 + 5) = 4 + 45 = 49 Common differences in each row = 3 Fifth row 34, 37, 40, 43, 46,.. Sixth row 49, 52, 55, 58, 61, 64… 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 …………………………. First term in the 20th row = 4 + 3(1 + 2 + 3 + 4 +……………. +19) = \(4+\frac{3\times19\times20}{2}=574\) Last term in the 20th row = 574 + 19 x 3 = 574 + 57 = 631

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

Answer»

4, 7, 13, 22, 34, 49,…….

(4, 4 + 3, 7 + 6, 13 + 9, 22 + 12, 34 + 15),

Generally it written as 4 + 3(1 + 2 + 3 + ………..)

First term in the fifth row = 4 + 3(1 + 2 + 3 + 4) = 4 + 30 = 34

First term in the sixth row = 4 + 3(1 + 2 + 3 + 4 + 5) = 4 + 45 = 49

Common differences in each row = 3

Fifth row 34, 37, 40, 43, 46,..

Sixth row 49, 52, 55, 58, 61, 64…

7 10

13 16 19

22 25 28 31

34 37 40 43 46

49 52 55 58 61 64 ………………………….

First term in the 20th row = 4 + 3(1 + 2 + 3 + 4 +……………. +19)

= \(4+\frac{3\times19\times20}{2}=574\)

Last term in the 20th row = 574 + 19 x 3 = 574 + 57 = 631

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