Geometric progression (also known as a geometric sequence) is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
If the first term of the sequence is 'a' and the common ratio is 'r', then the nth term of the sequence is given by arn-1. General geometric progression can be written as:
a, ar, ar2, ar3, ar4, . . . , arn-1
Finance
The concept of geometric progression is a cornerstone in finance, used widely for forecasting and planning financial growth and strategies. Financial analysts leverage geometric progressions extensively to decipher potential growth trends for investments and generate substantial financial forecasts.
For example, imagine you invest ₹1,000 into a savings account compounding interest annually at a rate of 5%. Initially, your balance is ₹1,000. After a year, the balance isn't just ₹1,000 plus 5% of ₹1,000; instead, the interest is calculated on the balance of ₹1,000 plus the interest already accrued, i.e., (₹1,000 + ₹50).
Therefore, after one year, your deposit has risen to ₹1,000 × 1.05 = ₹1,050.
In the second year, you're earning interest not just on your initial principal amount of ₹1,000, but also on the ₹50 interest accumulated in the first year. So, at the end of the second year, the amount in the account would be ₹1,050 × 1.05 = ₹1,102.50
Medicine
In pharmacokinetics, drug concentration in the body follows a predictable pattern based on its half-life. Suppose a drug has a half-life of 4 hours and an initial dose of 400 mg is given. After 4 hours, 200 mg remains. Adding another 400 mg increases the total to 600 mg.
After the next 4 hours, 300 mg remains, and with another 400 mg dose, the total becomes 700 mg. This process continues, forming a pattern such as 400, 600, 700, …
Although not a strict geometric progression, it shows a consistent pattern of decay and accumulation. This helps doctors determine appropriate dosage intervals to maintain an effective drug concentration in the body.