Answer:
38. [tex]a_1=107,\ a_n=a_{n-1}-1[/tex]
40. [tex]a_1=87,\ a_n=a_{n-1}+52[/tex]
Step-by-step explanation:
38. Given explicit formula:
[tex]a_n=108-n[/tex]
When [tex]n=1,[/tex] then [tex]a_1=108-1=107[/tex]
When [tex]n=2,[/tex] then [tex]a_2=108-2=106[/tex]
When [tex]n=3,[/tex] then [tex]a_3=108-3=105[/tex]
When [tex]n=4,[/tex] then [tex]a_4=108-4=104[/tex]
and so on
You can see that each next number is 1 less than previous number, so the recursive formula is
[tex]a_n=a_{n-1}-1[/tex]
40. Given explicit formula:
[tex]a_n=35+52n[/tex]
When [tex]n=1,[/tex] then [tex]a_1=35+52\cdot 1=87[/tex]
When [tex]n=2,[/tex] then [tex]a_2=35+52\cdot 2=139[/tex]
When [tex]n=3,[/tex] then [tex]a_3=35+52\cdot 3=191[/tex]
When [tex]n=4,[/tex] then [tex]a_4=35+52\cdot 4=243[/tex]
and so on
You can see that each next number is 52 more than previous number, so the recursive formula is
[tex]a_n=a_{n-1}+52[/tex]
