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

Answer:

The common difference of the progression is 3.

Step-by-step 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.

⇒ $\frac{-8+6d}{-8+8d} =\frac{5}{8}$                    ...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.

⇒ $8d=24$

⇒ $d=\frac{24}{8} =3$                    ...dividing both sides with 3.

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