In real life, the formula (a_n = a_1 \cdot r^{(n - 1)}) is really useful for understanding geometric sequences.
Financial Growth:
Let’s say you invest $1,000, and it earns 5% interest each year ((r = 1.05)).
The amount of money you will have after (n) years can be found using this formula:
(a_n = 1000 \cdot (1.05)^{(n - 1)}).
Population Growth:
Think about a culture of bacteria that doubles in size every hour ((r = 2)).
If you start with 100 bacteria, you can use this formula:
(a_n = 100 \cdot 2^{(n - 1)}).
These examples show how the formula works in real-life situations!
In real life, the formula (a_n = a_1 \cdot r^{(n - 1)}) is really useful for understanding geometric sequences.
Financial Growth:
Let’s say you invest $1,000, and it earns 5% interest each year ((r = 1.05)).
The amount of money you will have after (n) years can be found using this formula:
(a_n = 1000 \cdot (1.05)^{(n - 1)}).
Population Growth:
Think about a culture of bacteria that doubles in size every hour ((r = 2)).
If you start with 100 bacteria, you can use this formula:
(a_n = 100 \cdot 2^{(n - 1)}).
These examples show how the formula works in real-life situations!