Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20?
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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 , ....
I hope this will useful to you.
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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 , ....
I hope this will useful to you.
******
please mark as BRAINliest answer
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Answered by
7
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 , ....
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