In an arithmetic sequence d represent the common difference.
The formula to find the general term of an arithmetic sequence is,
[tex] a_{n} =a_{1} +(n-1)d [/tex]
Where [tex] a_{n} [/tex]= nth term and
[tex] a_{1} [/tex] = First term.
Given, [tex] a_{5} = 24, a_{9} = 40 [/tex]. Therefore,
[tex] a_{1} +(5-1)d = 24 , a_{1} +(9-1)d = 40 [/tex]
[tex] a_{1} +4d = 24 , a_{1} +8d = 40 [/tex]
Next step is to subtract the above equations so that we can eliminate a1 and get the value of d. Hence,
4d - 8d = 24 - 40
-4d = - 16
[tex] \frac{-4d}{-4}= \frac{-16}{-4} [/tex] Divide each sides by - 16.
d = 4
So, d = 4.
Hope this helps yoi!.
