Answer: After 30 days, you would have $30,000
Step-by-step explanation: The question clearly gives us a progression which is best described as an arithmetic progression, that is, every term (or every day's amount of money) is determined by adding a fixed amount to what you already have from the previous term (or previous day).
In order to determine the amount earned after a given number of days, we will begin by determining a formula that can be suited for calculating all through any given number of days.
The first amount is fixed already, and we shall call that a. So a equals 1000. The amount added to that is 1000, so for day 2, you shall have 1000 plus 1000 which gives you 2000. The amount added we shall call d, so for day one you earned 1000, for day two you earned 1000 plus 1000. For day three you will earn 2000 plus 1000, which gives you 3000.
Having taken day one as a, and each successive 1000 as d, observe the following trend;
Day 1 = a
Day 2 = a + d
Day 3 = a + (3 - 1)d which gives you a + 2d
Since the first day has been represented by a, the third day shall be less by one common difference which is d. Hence the formula for day n can be expressed as follows;
Day ₙ = a + (n - 1)d
Where n is the number of days, the nth day shall be less by 1 since the term already includes day 1, which is the first term, hence every term shall always be less by 1. In other words, the 30th day (or 30th term) shall be less by 1 shown as follows
Day 30 = 1000 + (30 - 1) 1000
Day 30 = 1000 + (29 x 1000)
Day 30 = 1000 + 29000
Day 30 = 30000
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