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 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 infinite GP when r is less than one
Sum of First n terms=First term/(1-Common Ratio) 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 of first n terms in a finite GP Formula

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

Sum of first n terms in a finite GP calculator uses Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1) to calculate the Sum of First n terms, Sum of first n terms in a finite GP is the total of first n terms of geometric progression having finite number of terms in it. For eg- 2,4,8,16,32,64. This GP with common ratio 2 has 6 terms in it and sum of its first 3 terms is 14. . Sum of First n terms and is denoted by Sn symbol.

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

FAQ

What is Sum of first n terms in a finite GP?
Sum of first n terms in a finite GP is the total of first n terms of geometric progression having finite number of terms in it. For eg- 2,4,8,16,32,64. This GP with common ratio 2 has 6 terms in it and sum of its first 3 terms is 14. and is represented as Sn=(a*((r^n)-1))/(r-1) or Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-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 Sum of first n terms in a finite GP?
Sum of first n terms in a finite GP is the total of first n terms of geometric progression having finite number of terms in it. For eg- 2,4,8,16,32,64. This GP with common ratio 2 has 6 terms in it and sum of its first 3 terms is 14. is calculated using Sum of First n terms=(First term*((Common Ratio^value of n)-1))/(Common Ratio-1). To calculate Sum of first n terms in a finite 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 Sum of First n terms?
In this formula, Sum of First n terms uses First term, Common Ratio and value of n. 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/(1-Common Ratio)
  • 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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