LCM of two numbers

Sum of Infinite Arithmetic Geometric Progression Calculator

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AP,GP and HP General Series Mean

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Arithmetic Geometric Progression Important Formulas of AP, GP and HP Arithmetic Progression Geometric Progression More >>

✖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 Infinite Progression is the ratio of any term to its preceding term of an Infinite Progression.ⓘ Common Ratio of Infinite Progression [r_∞]			+10% -10%
✖The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.ⓘ Common Difference of Progression [d]			+10% -10%

✖The Sum of Infinite Progression is the summation of the terms starting from the first term to the infinite term of given infinite Progression.ⓘ Sum of Infinite Arithmetic Geometric Progression [S_∞]

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Sum of Infinite Arithmetic Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Infinite Progression = (First Term of Progression/(1-Common Ratio of Infinite Progression))+((Common Difference of Progression*Common Ratio of Infinite Progression)/(1-Common Ratio of Infinite Progression)^2)
S_∞ = (a/(1-r_∞))+((d*r_∞)/(1-r_∞)^2)
This formula uses 4 Variables

Variables Used

Sum of Infinite Progression - The Sum of Infinite Progression is the summation of the terms starting from the first term to the infinite term of given infinite Progression.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
Common Ratio of Infinite Progression - The Common Ratio of Infinite Progression is the ratio of any term to its preceding term of an Infinite Progression.
Common Difference of Progression - The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

STEP 1: Convert Input(s) to Base Unit

First Term of Progression: 3 --> No Conversion Required
Common Ratio of Infinite Progression: 0.8 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_∞ = (a/(1-r_∞))+((d*r_∞)/(1-r_∞)^2) --> (3/(1-0.8))+((4*0.8)/(1-0.8)^2)

Evaluating ... ...

S_∞ = 95

STEP 3: Convert Result to Output's Unit

95 --> No Conversion Required

FINAL ANSWER

95 <-- Sum of Infinite Progression

(Calculation completed in 00.004 seconds)

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Created by Mayank Tayal

National Institute of Technology (NIT), Durgapur

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Indian Institute of Information Technology (IIIT), Bhopal

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< Arithmetic Geometric Progression Calculators

Sum of First N Terms of Arithmetic Geometric Progression

LaTeX Go Sum of First N Terms of Progression = ((First Term of Progression-((First Term of Progression+(Index N of Progression-1)*Common Difference of Progression)*Common Ratio of Progression^(Index N of Progression)))/(1-Common Ratio of Progression))+(Common Difference of Progression*Common Ratio of Progression*(1-Common Ratio of Progression^(Index N of Progression-1))/(1-Common Ratio of Progression)^2)

Sum of Infinite Arithmetic Geometric Progression

LaTeX Go Sum of Infinite Progression = (First Term of Progression/(1-Common Ratio of Infinite Progression))+((Common Difference of Progression*Common Ratio of Infinite Progression)/(1-Common Ratio of Infinite Progression)^2)

Nth Term of Arithmetic Geometric Progression

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

< Arithmetic Geometric Progression Calculators

Sum of First N Terms of Arithmetic Geometric Progression

Sum of Infinite Arithmetic Geometric Progression

Nth Term of Arithmetic Geometric Progression

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

Sum of Infinite Arithmetic Geometric Progression Formula

LaTeX Go

What is an Arithmetic Geometric Progression?

An Arithmetic Geometric Progression or simply AGP, is basically a combination of an Arithmetic Progression and a Geometric Progression as name indicates. Mathematically, an AGP is obtained by taking the product of each term of an AP with the corresponding term of a GP. That is, an AGP is of the form a1b1, a2b2, a3b3,... where a1, a2, a3,... is an AP and b1, b2, b3,... is a GP. If d is the common difference and a is the first term of the AP, and r is the common ratio of the GP then the nth term of the AGP will be (a + (n-1)d)(r^(n-1)).

How to Calculate Sum of Infinite Arithmetic Geometric Progression?

Sum of Infinite Arithmetic Geometric Progression calculator uses Sum of Infinite Progression = (First Term of Progression/(1-Common Ratio of Infinite Progression))+((Common Difference of Progression*Common Ratio of Infinite Progression)/(1-Common Ratio of Infinite Progression)^2) to calculate the Sum of Infinite Progression, The Sum of Infinite Arithmetic Geometric Progression is the summation of the terms starting from the first term to the infinite term of given Arithmetic Geometric Progression. Sum of Infinite Progression is denoted by S_∞ symbol.

How to calculate Sum of Infinite Arithmetic Geometric Progression using this online calculator? To use this online calculator for Sum of Infinite Arithmetic Geometric Progression, enter First Term of Progression (a), Common Ratio of Infinite Progression (r_∞) & Common Difference of Progression (d) and hit the calculate button. Here is how the Sum of Infinite Arithmetic Geometric Progression calculation can be explained with given input values -> 95 = (3/(1-0.8))+((4*0.8)/(1-0.8)^2).

FAQ

What is Sum of Infinite Arithmetic Geometric Progression?

The Sum of Infinite Arithmetic Geometric Progression is the summation of the terms starting from the first term to the infinite term of given Arithmetic Geometric Progression and is represented as S_∞ = (a/(1-r_∞))+((d*r_∞)/(1-r_∞)^2) or Sum of Infinite Progression = (First Term of Progression/(1-Common Ratio of Infinite Progression))+((Common Difference of Progression*Common Ratio of Infinite Progression)/(1-Common Ratio of Infinite Progression)^2). The First Term of Progression is the term at which the given Progression starts, The Common Ratio of Infinite Progression is the ratio of any term to its preceding term of an Infinite Progression & The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

How to calculate Sum of Infinite Arithmetic Geometric Progression?

The Sum of Infinite Arithmetic Geometric Progression is the summation of the terms starting from the first term to the infinite term of given Arithmetic Geometric Progression is calculated using Sum of Infinite Progression = (First Term of Progression/(1-Common Ratio of Infinite Progression))+((Common Difference of Progression*Common Ratio of Infinite Progression)/(1-Common Ratio of Infinite Progression)^2). To calculate Sum of Infinite Arithmetic Geometric Progression, you need First Term of Progression (a), Common Ratio of Infinite Progression (r_∞) & Common Difference of Progression (d). With our tool, you need to enter the respective value for First Term of Progression, Common Ratio of Infinite Progression & Common Difference 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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