Question

Determine an A.P. whose fifth term is 19 and the difference of the 8th term from the 13th term is 20.

Answer 1

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

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

i) Given t₅ = 19

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

ii ) differnce of the eighth term from

the thirteeth term = 20

t₁₃ - t₈ = 20

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

a + 12d - a - 7d = 20

5d = 20

d = 4

Put d = 5 in ( 2 )

a + 4d = 19

a + 4 × 4 = 19

a + 16= 19

a = 19 - 16

a =3

Therefore,
a = 3 , d =4

Required A .P is

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

3 , 7 , 11 , 15, 19 , ....