Geometric Sequence Growth Calculator

How to calculate a geometric sequence?

A geometric sequence is a series of numbers where each term after the first is determined by multiplying the preceding term by a fixed, non-zero constant called the common ratio. This mathematical progression results in rapid growth or decay.

N-th Term: aₙ = a₁ * r^(n-1)
Sum of n Terms: Sₙ = a₁ * (1 - rⁿ) / (1 - r)

Using the Geometric Sequence calculator: an example

To illustrate, consider a sequence where the starting value a₁ = 5, the common ratio r = 2, and we want to find results for the n = 4 term.

Step-by-step calculation:

• 4th Term (a₄): 5 * 2^(4-1) = 5 * 2³ = 5 * 8 = 40
• Sum of 4 Terms (S₄): 5 * (1 - 2⁴) / (1 - 2) = 5 * (1 - 16) / (-1) = 5 * (-15) / (-1) = 75

Frequently Asked Questions

What is a common ratio?
The common ratio is the constant value multiplied by each term to produce the next term in the sequence.

What happens if r is 1?
If the common ratio is 1, the sequence becomes constant where every term is equal to the first term, as you are simply multiplying by one.

Can a geometric sequence decrease?
Yes, a sequence decreases (decays) when the common ratio is between 0 and 1, causing each subsequent term to be smaller than the previous one.