What Is A Geometric Sequence Example?
What is a Geometric Sequence Example?
A Geometric Sequence Example is a sequence of numbers where each number is the product of the previous number and a common ratio. This means that each number in the sequence is obtained by multiplying the previous number by a fixed number. The fixed number is called the common ratio.
Geometric Sequence Example
Here are three examples of geometric sequences with a common ratio of two:
- 1, 2, 4, 8, 16, 32, 64, 128, 256, 512…
- 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024…
- 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048…
Calculating a Geometric Series
To calculate the sum of a geometric series, you will need to know the first number in the series, the common ratio and the number of terms in the series. The formula for calculating the sum of a geometric series is:
sum = a * (1 – r^n) / (1 – r)
Where a is the first number in the sequence, r is the common ratio, and n is the number of terms in the series.
Let’s calculate the sum of the first 10 terms of the geometric sequence with a first term of 4 and a common ratio of 2.
a = 4, r = 2, n = 10
sum = 4 * (1 – 2^10) / (1 – 2)
sum = 4 * (1 – 1024) / -1
sum = -1020
A geometric sequence example is a sequence of numbers where each number is the product of the previous number and a common ratio. The sum of a geometric sequence can be calculated using a simple formula. With this knowledge, you can easily calculate the sum of any geometric sequence.