Question

Write a recursive formula for each explicit formula

Answer 1

Answer:

38. $a_1=107,\ a_n=a_{n-1}-1$

40. $a_1=87,\ a_n=a_{n-1}+52$

Step-by-step explanation:

38. Given explicit formula:

$a_n=108-n$

When $n=1,$ then $a_1=108-1=107$

When $n=2,$ then $a_2=108-2=106$

When $n=3,$ then $a_3=108-3=105$

When $n=4,$ then $a_4=108-4=104$

and so on

You can see that each next number is 1 less than previous number, so the recursive formula is

$a_n=a_{n-1}-1$

40. Given explicit formula:

$a_n=35+52n$

When $n=1,$ then $a_1=35+52\cdot 1=87$

When $n=2,$ then $a_2=35+52\cdot 2=139$

When $n=3,$ then $a_3=35+52\cdot 3=191$

When $n=4,$ then $a_4=35+52\cdot 4=243$

and so on

You can see that each next number is 52 more than previous number, so the recursive formula is

$a_n=a_{n-1}+52$