Answer: the deposit on January 9 will be $6561
Explanation:
Suppose you deposit
one cent on January 1,
three cents on January 2,
nine cents on January 3, and so on, since you are tripling the amount of your deposit each day, the amount of money each day is increasing in geometric progression.
The formula for the nth term, Tn of a geometric progression is
Tn = ar^n-1
Where
a is the first term of the sequence
n is the number of terms of the sequence
r is the common ratio
From the information given
a = 1(amount deposited on January 1)
r = 3(the rate at which the amount is increasing)
n = 9(9 days from January 1 to January 9)
T9 = amount on January 9.
It becomes
T9 = 1 × 3^(9-1) = 3^8
T9 = $6561