the first term of an arithmetic progression is -8 the ratio of the 7th term to the 9th term is 5 ratio 8 calculate the common difference of the progression

Answer 1

given: a = -8
a+6d : a + 8d = 5 : 8

(-8 + 6d)/(-8 + 8d) = 5/8
-64 + 48d = -40 + 40d
8d = 24
d = 3

check:
terms are
-8, -5, -2, 1, 4, 7, 10, 13, 16

term(7) : term(9) = 10 : 16 = 5 : 8 , as required