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
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
Nth term of GP
Nth term=First term*(Common Ratio^(value of n-1)) GO

10 Other formulas that calculate the same Output

Sum of first n terms of AGP
Sum of First n terms=((First term-(First term+(total terms-1)*Common difference)*(Common Ratio^total terms))/(1-Common Ratio))+(Common difference*Common Ratio*(1-Common Ratio^(total terms-1))/(1-Common Ratio)^2) GO
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 where r>1
Sum of First n terms=First term*(((Common Ratio^total terms)-1)/(Common Ratio-1)) 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
Sum of squares of first n natural numbers
Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6 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
Sum of cubes of first n natural numbers
Sum of First n terms=((value of n*(value of n+1))^2)/4 GO
Sum of first n natural numbers
Sum of First n terms=(value of n*(value of n+1))/2 GO
Sum of first n even natural numbers
Sum of First n terms=(value of n*(value of n+1)) GO
Sum of first n odd natural numbers
Sum of First n terms=(value of n)^2 GO

Sum infinite GP when r is less than one Formula

Sum of First n terms=First term/(1-Common Ratio)
S<sub>n</sub>=a/(1-r)
More formulas
Nth term of GP GO
Sum of first n terms in a finite GP 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 infinite GP?

An infinite GP is a GP with infinite number of terms.When the ratio has a magnitude greater than 1, the terms in the sequence will get larger and larger, and the if you add larger and larger numbers forever, you will get infinity for an answer.So, when common ratio r is less than 1, then only the above formula is applicable.

How to Calculate Sum infinite GP when r is less than one?

Sum infinite GP when r is less than one calculator uses Sum of First n terms=First term/(1-Common Ratio) to calculate the Sum of First n terms, Sum infinite GP when r is less than one is the sum of all the terms in a geometric progression which contains infinite terms. . Sum of First n terms and is denoted by Sn symbol.

How to calculate Sum infinite GP when r is less than one using this online calculator? To use this online calculator for Sum infinite GP when r is less than one, enter First term (a) and Common Ratio (r) and hit the calculate button. Here is how the Sum infinite GP when r is less than one calculation can be explained with given input values -> -1 = 1/(1-2).

FAQ

What is Sum infinite GP when r is less than one?
Sum infinite GP when r is less than one is the sum of all the terms in a geometric progression which contains infinite terms. and is represented as Sn=a/(1-r) or Sum of First n terms=First term/(1-Common Ratio). First term is the initial term of a series or any sequence like arithmetic progression, geometric progression etc. It is generally denoted with 'a'. and Common Ratio is the constant factor between consecutive terms of a geometric sequence.
How to calculate Sum infinite GP when r is less than one?
Sum infinite GP when r is less than one is the sum of all the terms in a geometric progression which contains infinite terms. is calculated using Sum of First n terms=First term/(1-Common Ratio). To calculate Sum infinite GP when r is less than one, you need First term (a) and Common Ratio (r). With our tool, you need to enter the respective value for First term and Common Ratio 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 Sum of First n terms?
In this formula, Sum of First n terms uses First term and Common Ratio. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Sum of First n terms=(total terms/2)*(2*First term+(total terms-1)*Common difference)
  • Sum of First n terms=(total terms/2)*(First term+Last term)
  • Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1)
  • Sum of First n terms=(value of n*(value of n+1))/2
  • Sum of First n terms=(value of n*(value of n+1)*(2*value of n+1))/6
  • Sum of First n terms=((value of n*(value of n+1))^2)/4
  • Sum of First n terms=First term*(((Common Ratio^total terms)-1)/(Common Ratio-1))
  • Sum of First n terms=((First term-(First term+(total terms-1)*Common difference)*(Common Ratio^total terms))/(1-Common Ratio))+(Common difference*Common Ratio*(1-Common Ratio^(total terms-1))/(1-Common Ratio)^2)
  • Sum of First n terms=(value of n*(value of n+1))
  • Sum of First n terms=(value of n)^2
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