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in Arithmetic Sequences by (30.5k points)
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Write the next two lines of the pattern above. Calculate the first and last terms of the 20th line.

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Best 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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