Respuesta :
Answer:
[tex]a_{n+1} = a_n + 5[/tex]
Step-by-step explanation:
We are given the following in the question:
An arithmetic sequence where 5 is added to every term.
Thus, common difference, d = 5
Let the first term be
[tex]a = a_0[/tex]
Then, [tex]n^{th}[/tex] term of an arithmetic sequence is given by:
[tex]a_n = a_0 + (n-1)d[/tex]
Putting values, we get,
[tex]a_n = a_0 + (n-1)5\\a_n = a_0 + 5n - 5\\a_{n+1} = a_0 + (n+1-1)5\\a_{n+1} = a_0 + (n-1)5 + 5\\a_{n+1} = a_n + 5[/tex]
is the required recursive relation for arithmetic progression.
