Nth term of GP Calculator

Category	Math ↺
Math	Sequence and Series ↺
Sequence-And-Series	Geometric Progression ↺

✖First term is the initial term of a series or any sequence like arithmetic progression, geometric progression etc. It is generally denoted with 'a'. ⓘ First term [a]			+10% -10%
✖Common Ratio is the constant factor between consecutive terms of a geometric sequence.ⓘ Common Ratio [r]			+10% -10%
✖value of n is the index value of position n in a series or a sequence.ⓘ value of n [n]			+10% -10%

✖Nth term is particular term at index/position n (by default from beginning).ⓘ Nth term of GP [a_n]

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Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has created this Calculator and 100+ more calculators!

Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 200+ more calculators!

< 11 Other formulas that you can solve using the same Inputs

Sum of first n terms in an AP when common difference is given

Sum of First n terms=(total terms/2)*(2*First term+(total terms-1)*Common difference) GO

Sum of first n terms in a finite GP

Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1) GO

Position of pth term when pth term, first term & common difference is given

Position in series p=((pth Term-First term)/Common difference)+1 GO

Common Difference when first term & pth term are given

Common difference=(pth Term-First term)/(Position in series p-1) GO

Number of terms when Sum of first n terms, first term & last term are given

total terms=((2*Sum of First n terms)/(First term+Last term)) GO

Sum of first n terms in an AP when last term is given

Sum of First n terms=(total terms/2)*(First term+Last term) GO

Common Difference when first term, last term & number of terms are given

Common difference=((Last term-First term)/(total terms-1)) GO

Last term when number of terms, first term & common difference are given

Last term=((total terms-1)*Common difference)+First term GO

Number of terms of in an Arithematic Progression

total terms=((Last term-First term)/Common difference)+1 GO

Nth term of an Arithematic Progression

Nth term=First term+(total terms-1)*Common difference GO

Nth term of AP

Nth term=First term+(term number-1)*Common difference GO

< 8 Other formulas that calculate the same Output

Calculate nth term of AP when pth & qth terms are given

Nth term=((pth Term*(Position in series q-1)-qth Term*(Position in series p-1))/(Position in series q-Position in series p))+(total terms-1)*((qth Term-pth Term)/(Position in series q-Position in series p)) GO

Nth term of AGP

Nth term=(First term+((total terms-1)*Common difference))*(Common Ratio^(total terms-1)) GO

nth term from end in a finite GP

Nth term=First term*(Common Ratio^(total terms-value of n)) GO

Nth term of a HP

Nth term=1/(First term+(total terms-1)*Common difference) GO

Nth term of an Arithematic Progression

Nth term=First term+(total terms-1)*Common difference GO

Nth term of AP

Nth term=First term+(term number-1)*Common difference GO

nth term from the end of finite GP when last term and common ratio is given

Nth term=Last term/(Common Ratio^(value of n-1)) GO

nth term in a geometric progression

Nth term=First term*(Common Ratio)^(Last term-1) GO

Nth term of GP Formula

Nth term=First term*(Common Ratio^(value of n-1))
a<sub>n</sub>=a*(r^(n-1))

More formulas

Sum of first n terms in a finite GP GO

Sum infinite GP when r is less than one GO

nth term from end in a finite GP GO

nth term from the end of finite GP when last term and common ratio is given GO

Common Ratio GO

Geometric Mean of two numbers GO

Sum of infinite GP except first n terms when r<1 GO

Geometric Mean when Harmonic Mean and Arithmetic Mean is given GO

What is GP?

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.

How to Calculate Nth term of GP?

Nth term of GP calculator uses Nth term=First term*(Common Ratio^(value of n-1)) to calculate the Nth term, Nth term of GP is the nth term in geometric sequence or geometric progression when first term and common ratio is given. Nth term and is denoted by a_n symbol.

How to calculate Nth term of GP using this online calculator? To use this online calculator for Nth term of GP, enter First term (a), Common Ratio (r) and value of n (n) and hit the calculate button. Here is how the Nth term of GP calculation can be explained with given input values -> 1 = 1*(2^(1-1)).

FAQ

What is Nth term of GP?

Nth term of GP is the nth term in geometric sequence or geometric progression when first term and common ratio is given and is represented as a_n=a*(r^(n-1)) or Nth term=First term*(Common Ratio^(value of n-1)). First term is the initial term of a series or any sequence like arithmetic progression, geometric progression etc. It is generally denoted with 'a'. , Common Ratio is the constant factor between consecutive terms of a geometric sequence and value of n is the index value of position n in a series or a sequence.

How to calculate Nth term of GP?

Nth term of GP is the nth term in geometric sequence or geometric progression when first term and common ratio is given is calculated using Nth term=First term*(Common Ratio^(value of n-1)). To calculate Nth term of GP, you need First term (a), Common Ratio (r) and value of n (n). With our tool, you need to enter the respective value for First term, Common Ratio and value of n and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Nth term?

In this formula, Nth term uses First term, Common Ratio and value of n. We can use 8 other way(s) to calculate the same, which is/are as follows -

Nth term=First term+(term number-1)*Common difference
Nth term=First term+(total terms-1)*Common difference
Nth term=((pth Term*(Position in series q-1)-qth Term*(Position in series p-1))/(Position in series q-Position in series p))+(total terms-1)*((qth Term-pth Term)/(Position in series q-Position in series p))
Nth term=First term*(Common Ratio^(total terms-value of n))
Nth term=Last term/(Common Ratio^(value of n-1))
Nth term=1/(First term+(total terms-1)*Common difference)
Nth term=(First term+((total terms-1)*Common difference))*(Common Ratio^(total terms-1))
Nth term=First term*(Common Ratio)^(Last term-1)

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