Answer:
[tex]a_n = a_o +(n-1) d[/tex]
[tex] 22.5 = 15 +(2-1) d[/tex]
[tex] d = 22.5-15 =7.5[/tex]
The general expression is:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
Step-by-step explanation:
For this case we have the following arithmetic sequence given:
15, 22.5, 30,37.5
In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:
[tex]a_n = a_o +(n-1) d[/tex]
Where [tex]a_n[/tex] is the nth term [tex]a_o[/tex] the initial value for the sequence and d the common difference. For this case we have that [tex]a_o =15[/tex]
And for the first term we have:
[tex] 15= 15 +(1-1)d[/tex]
For the second term we have this:
[tex] 22.5 = 15 +(2-1) d[/tex]
And solving for the value of d we got:
[tex] d = 22.5-15 =7.5[/tex]
And for the 3th term we have:
[tex] a_3= 15 +(3-1)*7.5 =30[/tex]
And for the 4th term
[tex]a_4 =15 +(4-1)*7.5 =37.5[/tex]
So then our expression is correct and would be given by:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
