Answer:
9. [tex]a_n=7+6n[/tex]
10. [tex]a_n=a_{n-1}+7[/tex]
Step-by-step explanation:
9. Given the sequence
[tex]13, 19, 25, ...[/tex]
In this sequence,
[tex]a_1=13\\ \\a_2=19\\ \\a_3=25\\ \\...[/tex]
Note that
[tex]a_2-a_1=19-13=6\\ \\a_3-a_2=25-19=6,[/tex]
then the common difference in this sequence is [tex]d=6[/tex]
You have
[tex]a_1=13\\ \\d=6,[/tex]
then the explicit formula is
[tex]a_n=a_1+(n-1)d\\ \\a_n=13+(n-1)\cdot 6\\ \\a_n=13+6n-6\\ \\a_n=7+6n[/tex]
10. Given the sequence
[tex]-10,-3, 4, 11, ...[/tex]
In this sequence,
[tex]a_1=-10\\ \\a_2=-3\\ \\a_3=4\\ \\a_4=11\\ \\...[/tex]
Note that
[tex]a_2-a_1=-10-(-3)=-10+3=-7\\ \\a_3-a_2=-3-4=-7\\ \\a_4-a_3=11-4=7,[/tex]
then the common difference in this sequence is [tex]d=7[/tex]
You have
[tex]a_1=-10\\ \\d=7,[/tex]
then the recursive formula is
[tex]a_n=a_{n-1}+d\\ \\a_n=a_{n-1}+7[/tex]
