If the 9th term of an A.P is five times the 5th term. Find the relationship between a and d?

2 answers

Nth = a (n -1)d
¡à 9th = a (9 - 1)d
9th = a 8d

5th = a (5 -1)d
5th = a 4d
9th term of an A.P is five times the 5th term
¡à 9th = a 8d = 5(a 4d)
a 8d = 5a 20d
a - 5a = 20d - 8d
-4a/-4 = 12d/-4
a = -3d = Relationship.
2a+d=0