Geometric Sequence Calculator with Graph Feature
About Geometric Sequence Calculator
Discover the world of mathematical progressions with our high-precision Geometric Sequence Calculator. Not only can you calculate the nth term and the sum of the first n terms of a geometric sequence with full step-by-step solution, but you can also visualize the progression with our integrated graph feature.
What Is a Geometric Sequence?
In the realm of mathematics, a geometric sequence, also known as a geometric progression, is a sequence of numbers where each term after the initial one is derived by multiplying the preceding term by a fixed, non-zero number termed the "common ratio." This unique characteristic sets geometric sequences apart from other mathematical sequences.
How to Calculate a Geometric Sequence?
If you're looking to find the nth term of a geometric sequence, the formula is:
an = a1rn-1
- an is the nth term.
- r stands for the common ratio.
- n is the position of the term in the sequence.
For instance, in a sequence where the first term a1 is 2 and the common ratio r is 3, the 7th term can be calculated as:
a7= 2 × 3(7-1) = 1458
The sum of the first 7 terms Sn = a1 + ...+ an = 2 * (1 - 37) /(1 - 3) = 2186
This mathematical concept has vast applications, especially in fields that involve exponential growth or decay, such as finance and biology.
A geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by a constant ratio. A geometric series, on the other hand, is the sum of the terms of a geometric sequence.
The common ratio of a geometric sequence can be determined by dividing any term in the sequence by its preceding term.