Sum of Total Terms of Geometric Progression Calculator

✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+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 Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.ⓘ Number of Total Terms of Progression [n_Total]			+10% -10%

✖The Sum of Total Terms of Progression is the summation of the terms starting from the first to the last term of given Progression.ⓘ Sum of Total Terms of Geometric Progression [S_Total]

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Formula

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Sum of Total Terms of Geometric Progression

Formula

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

Example

`"3069"=("3"*(("2")^("10")-1))/("2"-1)`

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Sum of Total Terms of Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
S_Total = (a*(r^(n_Total)-1))/(r-1)
This formula uses 4 Variables

Variables Used

Sum of Total Terms of Progression - The Sum of Total Terms of Progression is the summation of the terms starting from the first to the last term of given Progression.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
Common Ratio of Progression - The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.
Number of Total Terms of Progression - The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.

STEP 1: Convert Input(s) to Base Unit

First Term of Progression: 3 --> No Conversion Required
Common Ratio of Progression: 2 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_Total = (a*(r^(n_Total)-1))/(r-1) --> (3*(2^(10)-1))/(2-1)

Evaluating ... ...

S_Total = 3069

STEP 3: Convert Result to Output's Unit

3069 --> No Conversion Required

FINAL ANSWER

3069 <-- Sum of Total Terms of Progression

(Calculation completed in 00.004 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 Total Terms of Geometric Progression Formula

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 Total Terms of Geometric Progression?

Sum of Total Terms of Geometric Progression calculator uses 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) to calculate the Sum of Total Terms of Progression, The Sum of Total Terms of Geometric Progression formula is defined as the summation of the terms starting from the first to the last term of given Geometric Progression. Sum of Total Terms of Progression is denoted by S_Total symbol.

How to calculate Sum of Total Terms of Geometric Progression using this online calculator? To use this online calculator for Sum of Total Terms of Geometric Progression, enter First Term of Progression (a), Common Ratio of Progression (r) & Number of Total Terms of Progression (n_Total) and hit the calculate button. Here is how the Sum of Total Terms of Geometric Progression calculation can be explained with given input values -> 3069 = (3*(2^(10)-1))/(2-1).

FAQ

What is Sum of Total Terms of Geometric Progression?

The Sum of Total Terms of Geometric Progression formula is defined as the summation of the terms starting from the first to the last term of given Geometric Progression and is represented as S_Total = (a*(r^(n_Total)-1))/(r-1) or 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). The First Term of Progression is the term at which the given Progression starts, The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression & The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.

How to calculate Sum of Total Terms of Geometric Progression?

The Sum of Total Terms of Geometric Progression formula is defined as the summation of the terms starting from the first to the last term of given Geometric Progression is calculated using 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). To calculate Sum of Total Terms of Geometric Progression, you need First Term of Progression (a), Common Ratio of Progression (r) & Number of Total Terms of Progression (n_Total). With our tool, you need to enter the respective value for First Term of Progression, Common Ratio of Progression & Number of Total Terms 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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