Numbers
Calculadora de sucesión geométrica
Used by developers, writers, and creators worldwide.
A geometric sequence calculator builds a sequence in which each term is the previous one multiplied by a fixed common ratio. Enter the first term, the common ratio, and how many terms you want, and it lists the sequence, restates the parameters, gives the formula for the nth term, computes that nth term directly, and sums the whole sequence using the geometric series formula. Geometric sequences model anything that grows or shrinks by a constant factor, such as compound interest, population doublings, depreciation, and the powers behind musical octaves. Students use the tool to learn the nth-term and sum formulas and to check their work, while teachers use it to generate fresh examples. Seeing the listed terms next to the closed-form nth term makes the pattern click, and the running sum shows how quickly such series grow. Use it to explore a sequence or total a series.
Read the complete guide — 4 min read
Loading usage…
Free forever — no account required
How to use
- Choose your options above
- Click Generate
- Copy your result
Detailed instructions
- Enter the first term of the sequence.
- Enter the common ratio.
- Choose how many terms to generate.
- Click Generate to see the sequence, nth term, and sum.
Use Cases
- •Listing the terms of a geometric sequence
- •Finding the nth term without writing them all out
- •Summing a geometric series
- •Checking sequence and series homework
- •Modelling constant-factor growth or decay
Tips
- →A ratio above one grows; between zero and one shrinks.
- →A negative ratio alternates the sign of each term.
- →The nth term skips straight to any position.
- →The sum formula avoids adding terms one by one.
FAQ
what is the common ratio
It is the fixed number each term is multiplied by to get the next. A ratio above one makes the sequence grow, a ratio between zero and one makes it shrink, and a negative ratio makes the signs alternate.
how is the nth term found
The nth term equals the first term times the common ratio raised to the power n minus one. The tool computes it directly so you can jump to any term without listing all the ones before it.
how is the sum calculated
For a ratio other than one it uses the closed-form geometric series formula a times r to the n minus one, divided by r minus one. When the ratio is exactly one every term is equal, so the sum is simply the first term times n.
You might also like
Popular tools from other categories that share themes with this one.