How to Put Geometric Sequence in Calculator
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Reviewed by Calculator Editorial Team
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. Calculators can help you work with geometric sequences by computing terms, sums, and other properties. This guide explains how to input and calculate geometric sequences in a calculator.
What is a Geometric Sequence?
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. The general form of a geometric sequence is:
a, ar, ar², ar³, ..., arⁿ⁻¹
Where:
- a is the first term
- r is the common ratio
- n is the term number
For example, the sequence 3, 6, 12, 24 is a geometric sequence with first term 3 and common ratio 2.
How to Input a Geometric Sequence in a Calculator
To input a geometric sequence in a calculator, follow these steps:
- Identify the first term (a) and the common ratio (r) of the sequence.
- Enter these values into the calculator's input fields.
- Specify the number of terms you want to calculate.
- Click the calculate button to generate the sequence.
Tip
Most scientific and graphing calculators have a built-in geometric sequence function. Look for functions like seq( or geoseries(.
Geometric Sequence Formula
nth Term of a Geometric Sequence
The nth term of a geometric sequence is given by:
aₙ = a × r^(n-1)
Sum of the First n Terms
The sum of the first n terms of a geometric sequence is given by:
Sₙ = a × (1 - rⁿ) / (1 - r) (for r ≠ 1)
Sₙ = a × n (for r = 1)
Worked Example
Let's calculate the first 5 terms of a geometric sequence with first term 2 and common ratio 3.
| Term Number (n) | Term Value (aₙ) |
|---|---|
| 1 | 2 × 3^(0) = 2 |
| 2 | 2 × 3^(1) = 6 |
| 3 | 2 × 3^(2) = 18 |
| 4 | 2 × 3^(3) = 54 |
| 5 | 2 × 3^(4) = 162 |
The sequence is: 2, 6, 18, 54, 162.
The sum of the first 5 terms is: 2 + 6 + 18 + 54 + 162 = 242.
FAQ
What is the difference between an arithmetic and geometric sequence?
An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms.
How do I know if a sequence is geometric?
A sequence is geometric if the ratio between consecutive terms is constant. For example, in 5, 10, 20, 40, each term is multiplied by 2.
Can a geometric sequence have a negative common ratio?
Yes, a geometric sequence can have a negative common ratio. For example, 3, -6, 12, -24 has a common ratio of -2.