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,.... ,ar^{n - 1}

Infinite GP = a , ar, ar², ar³,....,ar^{n - 1},.....

Here, ar^n-1 denotes the n^th 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 ar^n-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

a_n = ar^{n - 1}

a₁(first term) = 6 × 2^{1 - 1}= 6

a₂(second term) = 6 × 2^{2 - 1}= 12

a₃(third term) = 6 × 2^{3 - 1}= 24

a₄(fourth term) = 6 × 2^{4 - 1}= 48

a₅(fifth term) = 6 × 2^{5 - 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

a_n = ar^{n - 1}

a₁(first term) = 125 × 0.25^{1 - 1}= 125

a₂(second term) = 125 × 0.25^{2 - 1}= 31.25

a₃(third term) = 125 × 0.25^{3 - 1}= 7.81

a₄(fourth term) = 125 × 0.25^{4 - 1}= 1.95

a₅(fifth term) = 125 × 0.25^{5 - 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

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