Answer:
Both sequence are same, so the given statement is true.
Step-by-step explanation:
The first sequence is defined as
[tex]a_n=5n+3[/tex] ..... (1)
The second sequence is defined as
[tex]a_1=8[/tex]
[tex]a_n=a_{n-1}+5[/tex]
It can be written as
[tex]a_n-a_{n-1}=5[/tex]
The common difference of the sequence is
[tex]d=a_n-a_{n-1}=5[/tex]
The first term of the sequence is 8 and common difference is 5.
The second sequence can defined as
[tex]a_n=a+(n-1)d[/tex]
[tex]a_n=8+(n-1)5[/tex]
[tex]a_n=8+5n-5[/tex]
[tex]a_n=5n+3[/tex] .....(2)
From (1) and (2), we can say that both sequence are same.
Therefore the given statement is true.
