Geometric Sequence Calculator
Geometric Sequence Calculator helps to compute the first five terms in a geometric sequence. A geometric sequence can also be called a geometric progression. Geometric progressions can be finite or infinite.
What is Geometric Sequence Calculator?
Geometric Sequence Calculator is an online tool that helps to calculate the first five terms in a geometric sequence when the first term and the common ratio are known. A geometric sequence is one where two consecutive terms have a constant ratio. To use the geometric sequence calculator, enter the values in the given input boxes.
Geometric Sequence Calculator
NOTE: Please enter the values up to two digits only.
How to Use Geometric Sequence Calculator?
Please follow the steps below to find the first few terms in a geometric sequence using the geometric sequence calculator:
- Step 1: Go to Cuemath's online geometric sequence calculator.
- Step 2: Enter the values in the given input boxes.
- Step 3: Click on the "Calculate" button to find the terms of the geometric sequence.
- Step 4: Click on the "Reset" button to clear the fields and enter new values.
How Does Geometric Sequence Calculator Work?
A geometric progression (GP) in which the last term is defined is known as a finite GP. If the last term of a GP is not defined it is known as an infinite GP. If the first term of a GP is given by "a", and the common ratio between two successive terms is given by r, then the GP is given as follows:
Finite GP = a , ar, ar2, ar3,.... ,arn - 1
Infinite GP = a , ar, ar2, ar3,....,arn - 1,.....
Here, arn-1 denotes the nth term of a GP. Given below are the steps to find the terms of a GP.
- Keep the first term, a, as it is.
- Multiply a by the common ratio r to get the second term; a × r.
- Multiply the second term by the common ratio to get the third term; ar × r = ar2
- Similarly, keep multiplying the common ratio with the previous term in order to determine the required number of terms.
- You can also substitute the value of n in arn-1 to find the various terms in a GP.
Solved Examples on Geometric Sequence
Example 1: Find the geometric sequence up to 5 terms if first term(a) = 6, and common ratio(r) = 2. Verify it using the online geometric sequence calculator.
Solution:
Given: a = 6, r = 2
an = arn - 1
a1(first term) = 6 × 21 - 1= 6
a2(second term) = 6 × 22 - 1= 12
a3(third term) = 6 × 23 - 1= 24
a4(fourth term) = 6 × 24 - 1= 48
a5(fifth term) = 6 × 25 - 1= 96
Therefore, the geometric sequence is {6, 12, 24, 48, 96, ...}
Example 2: Find the geometric sequence up to 5 terms if first term(a) = 125, and common ratio(r) = 1/4. Verify it using the online geometric sequence calculator.
Solution:
Given: a = 125, r = 1/4 = 0.25
an = arn - 1
a1(first term) = 125 × 0.251 - 1= 125
a2(second term) = 125 × 0.252 - 1= 31.25
a3(third term) = 125 × 0.253 - 1= 7.81
a4(fourth term) = 125 × 0.254 - 1= 1.95
a5(fifth term) = 125 × 0.255 - 1= 0.49
Therefore, the geometric sequence is {125, 31.25, 7.81, 1.95, 0.49, ...}
Similarly, you can try the geometric sequence calculator to find the terms of the geometric sequence for the following:
- First term(a) = 1, common ratio(r) = 1/2
- First term(a) = 5, common ratio(r) = 5
☛ Math Calculators:
visual curriculum