Write a recursive rule and an explicit rule for the arithmetic sequence 19,9,-1,-11, ...

the formula is an = a1+d (n-1)

where a1 is the first terms

d is the common difference

a1 = 19

d 1 = 9-19 = - 10

check: - 1-9 = - 10 the sequence goes down by 10

n is the term number

an = 19 - 10 (n-1)

we can distribute

an = 19 - 10n + 10

an = 29-10n

Check our work:

a4 = 29 - 10*4

= 29 - 40

= - 11

the 4th term is - 11 which 19,9,-1,-11, ... shows, so we are good

Answer: an = 19 - 10 (n-1) or an = 29-10n