We want to find an explicit equation for an arithmetic sequence.
The sequence is given by:
[tex]p_n = 65 + n*8[/tex]
And using this we will find:
[tex]p_{90} = 785[/tex]
------------------------------
The information that we have is:
[tex]p_n = p_{n - 1} + 8[/tex]
[tex]p_0 = 65[/tex]
Then, using that recursive relation, we will have:
[tex]p_1 = p_0 + 8 = 65 + 8 = 73[/tex]
[tex]p_2 = p_1 + 8 = p_0 + 8 + 8 = p_0 + 2*8[/tex]
Here we can see the general pattern, we will have that explicit formula is just:
[tex]p_n = p_o + n*8 = 65 + n*8[/tex]
From this, we can get:
[tex]p_{90} = 65 + 90*8 = 785[/tex]
If you want to learn more, you can read:
https://brainly.com/question/18109692
