Mayank Tayal
National Institute of Technology (NIT), Durgapur
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Alithea Fernandes
Don Bosco College of Engineering (DBCE), Goa
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11 Other formulas that you can solve using the same Inputs

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
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

6 Other formulas that calculate the same Output

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 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 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 terms of AGP Formula

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)
More formulas
Nth term of an Arithematic Progression GO
Number of terms of in an Arithematic Progression GO
Sum of first n terms in an AP when common difference is given GO
Sum of first n terms in an AP when last term is given GO
Calculate nth term of AP when pth & qth terms are given GO
Common Difference when first term & pth term are given GO
Position of pth term when pth term, first term & common difference is given GO
Last term when number of terms, first term & common difference are given GO
Common Difference when first term, last term & number of terms are given GO
Number of terms when Sum of first n terms, first term & last term are given GO
Common Difference when pth & qth terms are given GO
Sum of first n terms where r>1 GO
Nth term of a HP GO
Harmonic Mean of two numbers GO
Nth term of AGP GO
Sum of infinite AGP where (-1 < r < 1) GO

What is Arithematic Geometric Progression ?

In mathematics, an arithmetico–geometric sequence is the result of the term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression.

How to Calculate Sum of first n terms of AGP?

Sum of first n terms of AGP calculator uses 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) to calculate the Sum of First n terms, The Sum of first n terms of AGP formula is defined as ( ( 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 and is denoted by Sn symbol.

How to calculate Sum of first n terms of AGP using this online calculator? To use this online calculator for Sum of first n terms of AGP, enter First term (a), Common difference (d), total terms (total) and Common Ratio (r) and hit the calculate button. Here is how the Sum of first n terms of AGP calculation can be explained with given input values -> 0 = ((1-(1+((0)-1)*1)*(2^(0)))/(1-2))+(1*2*(1-2^((0)-1))/(1-2)^2).

FAQ

What is Sum of first n terms of AGP?
The Sum of first n terms of AGP formula is defined as ( ( 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 ) and is represented as Sn=((a-(a+(total-1)*d)*(r^total))/(1-r))+(d*r*(1-r^(total-1))/(1-r)^2) or 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). 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 difference is the difference between two successive terms of an arithmetic progression. It is denoted by 'd'. , total terms is the total number of terms in a particular series and Common Ratio is the constant factor between consecutive terms of a geometric sequence.
How to calculate Sum of first n terms of AGP?
The Sum of first n terms of AGP formula is defined as ( ( 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 ) is calculated using 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). To calculate Sum of first n terms of AGP, you need First term (a), Common difference (d), total terms (total) and Common Ratio (r). With our tool, you need to enter the respective value for First term, Common difference, total terms 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, Common difference, total terms and Common Ratio. We can use 6 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=First term/(1-Common Ratio)
  • Sum of First n terms=First term*(((Common Ratio^total terms)-1)/(Common Ratio-1))
  • Sum of First n terms=(value of n*(value of n+1))
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