Sum of first n terms of AGP Calculator

Category	Math ↺
Math	Algebra ↺
Algebra	Series & Progression ↺
Series-And-Progression	Arithematic-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%
✖total terms is the total number of terms in a particular series.ⓘ total terms [total]			+10% -10%
✖Common difference is the difference between two successive terms of an arithmetic progression. It is denoted by 'd'. ⓘ Common difference [d]			+10% -10%
✖Common Ratio is the constant factor between consecutive terms of a geometric sequence.ⓘ Common Ratio [r]			+10% -10%

✖Sum of First n terms denoted the sum of first n terms occuring in a progression like Arithematic Progression, Geometric Progression, Harmonic Progression.ⓘ Sum of first n terms of AGP [S_n]

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Mayank Tayal

National Institute of Technology (NIT), Durgapur

Mayank Tayal has created this Calculator and 0+ more calculators!

Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

Alithea Fernandes has verified this Calculator and 50+ more calculators!

< 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 S_n 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 S_n=((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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