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

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

✖total terms is the total number of terms in a particular series.ⓘ total terms [total]			+10% -10%
✖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%
✖Last term is simply the term at which a particular series or sequence line arithmetic progression or geometric progression ends. It is generally denotes by 'l'.ⓘ Last term [l]			+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 in an AP when last term is given [S_n]

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

Mayank Tayal

National Institute of Technology (NIT), Durgapur

Mayank Tayal has created this Calculator and 25+ more calculators!

Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

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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

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 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 an AP when last term is given Formula

Sum of First n terms=(total terms/2)*(First term+Last term)
S<sub>n</sub>=(total/2)*(a+l)

More formulas

Nth term of AP Go

Number of terms of in an Arithematic Progression Go

Sum of first n terms in an AP when common difference 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

First term when pth & qth terms are given Go

Sum of last n terms in a finite AP with last term given Go

Sum of last n terms in a finite AP with first term, total terms given Go

Sum of all terms from position p to position q in an AP Go

Arithmetic Mean of two numbers Go

Arithmetic Mean when Harmonic Mean and Geometric Mean is given Go

What is an Arithematic Progression ?

An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. For example, the sequence 1, 2, 3, 4, ... is an arithmetic progression with common difference 1. Second example: the sequence 3, 5, 7, 9, 11,... is an arithmetic progression.

How to Calculate Sum of first n terms in an AP when last term is given?

Sum of first n terms in an AP when last term is given calculator uses Sum of First n terms=(total terms/2)*(First term+Last term) to calculate the Sum of First n terms, The Sum of first n terms in an AP when last term is given formula is defines the sum of first n terms of an Arithematic Progression when number of terms, first term and last term are given. Sum of First n terms and is denoted by S_n symbol.

How to calculate Sum of first n terms in an AP when last term is given using this online calculator? To use this online calculator for Sum of first n terms in an AP when last term is given, enter total terms (total), First term (a) and Last term (l) and hit the calculate button. Here is how the Sum of first n terms in an AP when last term is given calculation can be explained with given input values -> 0 = ((0)/2)*(1+1).

FAQ

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

The Sum of first n terms in an AP when last term is given formula is defines the sum of first n terms of an Arithematic Progression when number of terms, first term and last term are given and is represented as S_n=(total/2)*(a+l) or Sum of First n terms=(total terms/2)*(First term+Last term). total terms is the total number of terms in a particular series, 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 Last term is simply the term at which a particular series or sequence line arithmetic progression or geometric progression ends. It is generally denotes by 'l'.

How to calculate Sum of first n terms in an AP when last term is given?

The Sum of first n terms in an AP when last term is given formula is defines the sum of first n terms of an Arithematic Progression when number of terms, first term and last term are given is calculated using Sum of First n terms=(total terms/2)*(First term+Last term). To calculate Sum of first n terms in an AP when last term is given, you need total terms (total), First term (a) and Last term (l). With our tool, you need to enter the respective value for total terms, First term and Last term 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 total terms, First term and Last term. 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=(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=(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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