Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has created this Calculator and 100+ more calculators!
Pragati Jaju
College Of Engineering (COEP), Pune
Pragati Jaju has verified this Calculator and 200+ 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

2 Other formulas that calculate the same Output

Sum of all terms from position p to position q in an AP
sum required=((value of q*(2*First term+Common difference*(value of q-1)))-((value of p-1)*(2*First term+Common difference*(value of p-2))))/2 GO
Sum of cubes of first n even numbers
sum required=2*(value of n*(value of n+1))^2 GO

Sum of infinite GP except first n terms when r<1 Formula

sum required=(First term/(1-Common Ratio))-(First term*((Common Ratio^total terms)-1))/(Common Ratio-1)
S<sub>n</sub>=(a/(1-r))-(a*((r^total)-1))/(r-1)
More formulas
Nth term of GP GO
Sum of first n terms in a finite 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
Geometric Mean when Harmonic Mean and Arithmetic Mean is given GO

Sum of Geometric Progressions depending upon the common ratio

For r=1, finite GP's sum can be calculated total terms*first terms as all the terms in GP will be same. For r>1, the sum of infinite GP will always be either positive infinity or negative infinity depending upon the nature of integers in it. For r<1, you can use the formula sum of infinite GP - sum of first n terms.

How to Calculate Sum of infinite GP except first n terms when r<1?

Sum of infinite GP except first n terms when r<1 calculator uses sum required=(First term/(1-Common Ratio))-(First term*((Common Ratio^total terms)-1))/(Common Ratio-1) to calculate the sum required, Sum of infinite GP except first n terms when r<1 is defined as the total sum of an infinite GP excluding the first n terms of it when common ratio is less then 1. sum required and is denoted by Sn symbol.

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

FAQ

What is Sum of infinite GP except first n terms when r<1?
Sum of infinite GP except first n terms when r<1 is defined as the total sum of an infinite GP excluding the first n terms of it when common ratio is less then 1 and is represented as Sn=(a/(1-r))-(a*((r^total)-1))/(r-1) or sum required=(First term/(1-Common Ratio))-(First term*((Common Ratio^total terms)-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 total terms is the total number of terms in a particular series.
How to calculate Sum of infinite GP except first n terms when r<1?
Sum of infinite GP except first n terms when r<1 is defined as the total sum of an infinite GP excluding the first n terms of it when common ratio is less then 1 is calculated using sum required=(First term/(1-Common Ratio))-(First term*((Common Ratio^total terms)-1))/(Common Ratio-1). To calculate Sum of infinite GP except first n terms when r<1, you need First term (a), Common Ratio (r) and total terms (total). With our tool, you need to enter the respective value for First term, Common Ratio and total terms 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 required?
In this formula, sum required uses First term, Common Ratio and total terms. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • sum required=((value of q*(2*First term+Common difference*(value of q-1)))-((value of p-1)*(2*First term+Common difference*(value of p-2))))/2
  • sum required=2*(value of n*(value of n+1))^2
Share Image
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!