Determine the AP whose 5th term is 19 and the difference of the 8th te

1.	Determine the AP whose 5th term is 19 and the difference of the 8th term from the 13thterm is 20.
Answer» Let a and d are first term and common difference of an A . P. nth term = tn = a + ( n - 1 )d----------( 1 ) i) Given t 5 = 19 a + 4d = 19 -------(2) ii ) differnce of the eighth term from the thirteeth term = 20 t 13 - t 8 = 20 a + 12d - ( a + 7d ) = 20 a + 12d - a - 7d = 20 5d = 20 d = 20/ 5 d = 5 Put d = 5 in ( 2 ) a + 4d = 19 a + 4 × 5 = 19 a + 20 = 19 a = 19 - 20 a = - 1 Therefore,a = -1 , d = 5 Required A .P is a , a+ d , a + 2d , a + 3d , ..... -1 , 4 , 9 , 14, 19 , ...

Determine the AP whose 5th term is 19 and the difference of the 8th term from the 13thterm is 20.

Answer»

Let a and d are first term and common difference of an A . P.

nth term = tn = a + ( n - 1 )d----------( 1 )

i) Given t 5 = 19

a + 4d = 19 -------(2)

ii ) differnce of the eighth term from

the thirteeth term = 20

t 13 - t 8 = 20

a + 12d - ( a + 7d ) = 20

a + 12d - a - 7d = 20

5d = 20

d = 20/ 5

d = 5

Put d = 5 in ( 2 )

a + 4d = 19

a + 4 × 5 = 19

a + 20 = 19

a = 19 - 20

a = - 1

Therefore,a = -1 , d = 5

Required A .P is

a , a+ d , a + 2d , a + 3d , .....

-1 , 4 , 9 , 14, 19 , ...