Question

determine the ap whose fifth term is 19 and difference of 18th term and 13th term is 20.

Answer 1

a+4d(5th term)=19

a+4d=19 ... (i)

18th term-13th term=20

a+17d-(a+12d)=20

a+17d-a-12d=20

5d=20

d=4

Put d=4 in (i)

a+4(4)=19

a+16=19

a=3

AP=3,7,11...

Answer 2

According to the Question

$\bf\huge a_{5} = 19$

a + 4d = 19 …. (1)

$\bf\huge a_{13} - a{8} = 20$

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

5d = 20

d = 4

Put value of d in (1) we get

a + 4(4) = 19

a = 19 - 16

a = 3

Therefore AP are 3, 7, 11, 15