Samantha loves collecting rare coins. In the first year of her collection, she starts with 50 rare coins. Each year after that, the number of coins she acquires is 30% more than the previous year.
Let g(n) represent the number of rare coins in Samantha's collection in the nth year since she began collecting.
a. Is it arithmetic or geometric?
b. Write in recursive formula.
a. It is a geometric sequence because each term is 30% more than the previous term.
b. The recursive formula for the number of rare coins in Samantha's collection in the nth year is:
g(n) = 1.3 * g(n-1), where g(1) = 50 and n > 1.