Question

The first term of an A.p is_8 the ratio of 7th to the 9th term is 5.8 calculate the common difference of the progression​

Answer 1

d = 3

Step-by-step 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 :

`a_n=a+(n-1)d`

ATQ,

`(a_7)/(a_9)=(5)/(8)\\\\(a+6d)/(a+8d)=(5)/(8)`

Put a = -8 in the above equation.

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

So, the common difference of the progression is 3.