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Sum of Infinite Arithmetic Geometric Progression Formula

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The Sum of Infinite Progression is the summation of the terms starting from the first term to the infinite term of given infinite Progression. Check FAQs

S ∞ = (\frac{a}{1 - r ∞}) + (\frac{d \cdot r ∞}{{(1 - r ∞)}^{2}})

S_∞ - Sum of Infinite Progression?a - First Term of Progression?r_∞ - Common Ratio of Infinite Progression?d - Common Difference of Progression?

Sum of Infinite Arithmetic Geometric Progression Example

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Here is how the Sum of Infinite Arithmetic Geometric Progression equation looks like with Values.

Here is how the Sum of Infinite Arithmetic Geometric Progression equation looks like with Units.

Here is how the Sum of Infinite Arithmetic Geometric Progression equation looks like.

95 = (\frac{3}{1 - 0.8}) + (\frac{4 \cdot 0.8}{{(1 - 0.8)}^{2}})

95 = (\frac{3}{1 - 0.8}) + (\frac{4 \cdot 0.8}{{(1 - 0.8)}^{2}})

95 = (\frac{3}{1 - 0.8}) + (\frac{4 \cdot 0.8}{{(1 - 0.8)}^{2}})

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Sum of Infinite Arithmetic Geometric Progression Solution

Follow our step by step solution on how to calculate Sum of Infinite Arithmetic Geometric Progression?

FIRST Step Consider the formula

S ∞ = (\frac{a}{1 - r ∞}) + (\frac{d \cdot r ∞}{{(1 - r ∞)}^{2}})

Next Step Substitute values of Variables

∴

S ∞ = (\frac{3}{1 - 0.8}) + (\frac{4 \cdot 0.8}{{(1 - 0.8)}^{2}})

Next Step Prepare to Evaluate

∴

S ∞ = (\frac{3}{1 - 0.8}) + (\frac{4 \cdot 0.8}{{(1 - 0.8)}^{2}})

LAST Step Evaluate

∴

S ∞ = 95

Sum of Infinite Arithmetic Geometric Progression Formula Elements

Variables

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.

Symbol: S_∞

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Sum of Infinite Progression

First Term of Progression

The First Term of Progression is the term at which the given Progression starts.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find First Term of Progression

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.

Symbol: r_∞

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 1.

Formulas to find Common Ratio of 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.

Symbol: d

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Common Difference of Progression

Other formulas in Arithmetic Geometric Progression category

Go Nth Term of Arithmetic Geometric Progression

T n = (a + ((n - 1) \cdot d)) \cdot (r^{n - 1})

Go Sum of First N Terms of Arithmetic Geometric Progression

S n = (\frac{a - ((a + (n - 1) \cdot d) \cdot r^{n})}{1 - r}) + (d \cdot r \cdot \frac{1 - r^{n - 1}}{{(1 - r)}^{2}})

How to Evaluate Sum of Infinite Arithmetic Geometric Progression?

Sum of Infinite Arithmetic Geometric Progression evaluator 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 evaluate 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 evaluate Sum of Infinite Arithmetic Geometric Progression using this online evaluator? To use this online evaluator 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.

FAQs on Sum of Infinite Arithmetic Geometric Progression

What is the formula to find Sum of Infinite Arithmetic Geometric Progression?

The formula of Sum of Infinite Arithmetic Geometric Progression is expressed as 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). Here is an example- 95 = (3/(1-0.8))+((4*0.8)/(1-0.8)^2).

How to calculate Sum of Infinite Arithmetic Geometric Progression?

With First Term of Progression (a), Common Ratio of Infinite Progression (r_∞) & Common Difference of Progression (d) we can find Sum of Infinite Arithmetic Geometric Progression using the formula - 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).

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Sum of Infinite Arithmetic Geometric Progression Formula

Sum of Infinite Arithmetic Geometric Progression Example

Sum of Infinite Arithmetic Geometric Progression Solution

Sum of Infinite Arithmetic Geometric Progression Formula Elements

Other formulas in Arithmetic Geometric Progression category

How to Evaluate Sum of Infinite Arithmetic Geometric Progression?

FAQs on Sum of Infinite Arithmetic Geometric Progression

Variable Name