Answer:
d = 3
Explanation:
The first term of the AP, a = -8
The ratio of 7th to the 9th term is 5.8.
We need to find the common difference of the progression.
The nth term of an AP is given by :
[tex]a_n=a+(n-1)d[/tex]
ATQ,
[tex]\dfrac{a_7}{a_9}=\dfrac{5}{8}\\\\\dfrac{a+6d}{a+8d}=\dfrac{5}{8}[/tex]
Put a = -8 in the above equation.
[tex]\dfrac{-8+6d}{-8+8d}=\dfrac{5}{8}\\\\-64+48d=-40+40d\\\\48d-40d=64-40\\\\8d=24\\\\d=3[/tex]
So, the common difference of the progression is 3.
