Question

The first term of an (AP) is-8.the ratio of the 7th term to the 9th term is 5:8 calculate the common difference of the progression​

Answer 1

The common difference of the progression is 3.

Explanation:

Given:

First term of the AP = (a) = -8

Ratio of 7th and 9th term = 5:8

So,

General term of an AP, Tn= a+(n-1)d

Where 'd' is the common difference.

`T_7=-8+(7-1)d` equation...(i)

`T_9=-8+(9-1)d` equation...(ii)

According to the question.

⇒
`(-8+6d)/(-8+8d) =(5)/(8)` ...cross-multiplying the terms.

⇒
`8(-8+6d)=5(-8+8d)`

⇒
`-64+48d=-40+40d`

⇒
`48d-40d=-40+64` ...subtracting 40d and adding 64 both sides.

⇒
`8d=24`

⇒
`d=(24)/(8) =3` ...dividing both sides with 3.

So the common difference of the progression is 'd' = 3.