Sum of Last N Terms of Geometric Progression Calculator

✖The Last Term of Progression is the term at which the given Progression terminates.ⓘ Last Term of Progression [l]			+10% -10%
✖The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.ⓘ Common Ratio of Progression [r]			+10% -10%
✖The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.ⓘ Index N of Progression [n]			+10% -10%

✖The Sum of Last N Terms of Progression is the summation of the terms starting from the end to the nth term of a given Progression.ⓘ Sum of Last N Terms of Geometric Progression [S_n(End)]

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Formula

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Sum of Last N Terms of Geometric Progression

Formula

`"S"_{"n(End)"} = ("l"*((1/"r")^"n"-1))/((1/"r")-1)`

Example

`"196.875"=("100"*((1/"2")^"6"-1))/((1/"2")-1)`

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Sum of Last N Terms of Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1)
S_n(End) = (l*((1/r)^n-1))/((1/r)-1)
This formula uses 4 Variables

Variables Used

Sum of Last N Terms of Progression - The Sum of Last N Terms of Progression is the summation of the terms starting from the end to the nth term of a given Progression.
Last Term of Progression - The Last Term of Progression is the term at which the given Progression terminates.
Common Ratio of Progression - The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.
Index N of Progression - The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

STEP 1: Convert Input(s) to Base Unit

Last Term of Progression: 100 --> No Conversion Required
Common Ratio of Progression: 2 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n(End) = (l*((1/r)^n-1))/((1/r)-1) --> (100*((1/2)^6-1))/((1/2)-1)

Evaluating ... ...

S_n(End) = 196.875

STEP 3: Convert Result to Output's Unit

196.875 --> No Conversion Required

FINAL ANSWER

196.875 <-- Sum of Last N Terms of Progression

(Calculation completed in 00.020 seconds)

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< 3 Sum of Terms of Geometric Progression Calculators

Sum of Total Terms of Geometric Progression

Go Sum of Total Terms of Progression = (First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression)-1))/(Common Ratio of Progression-1)

Sum of Last N Terms of Geometric Progression

Go Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1)

Sum of First N Terms of Geometric Progression

Go Sum of First N Terms of Progression = (First Term of Progression*(Common Ratio of Progression^Index N of Progression-1))/(Common Ratio of Progression-1)

< 9 Geometric Progression Calculators

Sum of Total Terms of Geometric Progression

Go Sum of Total Terms of Progression = (First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression)-1))/(Common Ratio of Progression-1)

Sum of Last N Terms of Geometric Progression

Go Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1)

Sum of First N Terms of Geometric Progression

Go Sum of First N Terms of Progression = (First Term of Progression*(Common Ratio of Progression^Index N of Progression-1))/(Common Ratio of Progression-1)

Nth Term from End of Geometric Progression

Go Nth Term from End of Progression = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression))

Number of Terms of Geometric Progression

Go Index N of Progression = log(Common Ratio of Progression,Nth Term of Progression/First Term of Progression)+1

First Term of Geometric Progression

Go First Term of Progression = Nth Term of Progression/(Common Ratio of Progression^(Index N of Progression-1))

Nth Term of Geometric Progression

Go Nth Term of Progression = First Term of Progression*(Common Ratio of Progression^(Index N of Progression-1))

Sum of Infinite Geometric Progression

Go Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression)

Common Ratio of Geometric Progression

Go Common Ratio of Progression = Nth Term of Progression/(N-1)th Term of Progression

Sum of Last N Terms of Geometric Progression Formula

Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1)
S_n(End) = (l*((1/r)^n-1))/((1/r)-1)

What is a Geometric Progression?

In Mathematics a Geometric Progression or simply GP 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 real number called the common ratio. For example, the sequence 2, 6, 18, 54,... is a Geometric Progression with common ratio 3. If the sum of all terms in the progression is a finite number or if the infinite sum of the progression exists then the we say it is an Infinite Geometric Progression or Infinite GP. And if the infinite sum of the progression does not exist, then it is a Finite Geometric Progression or Finite GP. If the absolute value of the common ratio is greater than 1 then the GP will be a Finite GP and if it is less than 1 then the GP will be an Infinite GP.

How to Calculate Sum of Last N Terms of Geometric Progression?

Sum of Last N Terms of Geometric Progression calculator uses Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1) to calculate the Sum of Last N Terms of Progression, The Sum of Last N Terms of Geometric Progression formula is defined as the summation of the terms starting from the end to the nth term of a given Geometric Progression. Sum of Last N Terms of Progression is denoted by S_n(End) symbol.

How to calculate Sum of Last N Terms of Geometric Progression using this online calculator? To use this online calculator for Sum of Last N Terms of Geometric Progression, enter Last Term of Progression (l), Common Ratio of Progression (r) & Index N of Progression (n) and hit the calculate button. Here is how the Sum of Last N Terms of Geometric Progression calculation can be explained with given input values -> 196.875 = (100*((1/2)^6-1))/((1/2)-1).

FAQ

What is Sum of Last N Terms of Geometric Progression?

The Sum of Last N Terms of Geometric Progression formula is defined as the summation of the terms starting from the end to the nth term of a given Geometric Progression and is represented as S_n(End) = (l*((1/r)^n-1))/((1/r)-1) or Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1). The Last Term of Progression is the term at which the given Progression terminates, The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression & The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

How to calculate Sum of Last N Terms of Geometric Progression?

The Sum of Last N Terms of Geometric Progression formula is defined as the summation of the terms starting from the end to the nth term of a given Geometric Progression is calculated using Sum of Last N Terms of Progression = (Last Term of Progression*((1/Common Ratio of Progression)^Index N of Progression-1))/((1/Common Ratio of Progression)-1). To calculate Sum of Last N Terms of Geometric Progression, you need Last Term of Progression (l), Common Ratio of Progression (r) & Index N of Progression (n). With our tool, you need to enter the respective value for Last Term of Progression, Common Ratio of Progression & Index N of Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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