Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Let the first term of an AP be a and common difference d.


Given


5th term, a5 = 19


And by using the nth term formula i.e. an = a + (n - 1)d


a + 4d = 19


a = 19 - 4d (eqn 1)


also,


20th term - 8th term = 20


a + 19d - (a + 7d) = 20


12d = 20



using this in eqn 1




So the AP is




5