Question

If the difference between the 7th and 9th terms

of an arithmetic sequence is 25. Find the
Common difference.​

Answer 1

The common difference is
`d=-(25)/(2)`

Step-by-step explanation:

The difference between the 7th and 9th terms of an arithmetic sequence is 25

Since, we know the general form of an AP is
`a_(n)=a_(1)+(n-1) d`

For
`n=7`, we have,

`a_(7)=a_(1)+(7-1) d`

`a_(7)=a_(1)+6 d` ---------(1)

For
`n=9`, we have,

`a_(9)=a_(1)+(9-1) d`

`a_(9)=a_(1)+8 d` ----------(2)

Subtracting (1) and (2), we get,

`a_7-a_9=6d-8d`

Since, it is given that the difference between 7th and 9th term is 25.

Hence, we have,

`25=-2d`

Dividing both sides by -2, we have,

`d=-(25)/(2)`

Hence, the common difference is
`d=-(25)/(2)`