The common difference is [tex]d=-\frac{25}{2}[/tex]
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 [tex]a_{n}=a_{1}+(n-1) d[/tex]
For [tex]n=7[/tex], we have,
[tex]a_{7}=a_{1}+(7-1) d[/tex]
[tex]a_{7}=a_{1}+6 d[/tex] ---------(1)
For [tex]n=9[/tex], we have,
[tex]a_{9}=a_{1}+(9-1) d[/tex]
[tex]a_{9}=a_{1}+8 d[/tex] ----------(2)
Subtracting (1) and (2), we get,
[tex]a_7-a_9=6d-8d[/tex]
Since, it is given that the difference between 7th and 9th term is 25.
Hence, we have,
[tex]25=-2d[/tex]
Dividing both sides by -2, we have,
[tex]d=-\frac{25}{2}[/tex]
Hence, the common difference is [tex]d=-\frac{25}{2}[/tex]
