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Sum of First N Terms of Arithmetic Geometric Progression Formula

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The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression. Check FAQs

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}})

S_n - Sum of First N Terms of Progression?a - First Term of Progression?n - Index N of Progression?d - Common Difference of Progression?r - Common Ratio of Progression?

Sum of First N Terms of Arithmetic Geometric Progression Example

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Here is how the Sum of First N Terms of Arithmetic Geometric Progression equation looks like with Values.

Here is how the Sum of First N Terms of Arithmetic Geometric Progression equation looks like with Units.

Here is how the Sum of First N Terms of Arithmetic Geometric Progression equation looks like.

1221 = (\frac{3 - ((3 + (6 - 1) \cdot 4) \cdot 2^{6})}{1 - 2}) + (4 \cdot 2 \cdot \frac{1 - 2^{6 - 1}}{{(1 - 2)}^{2}})

1221 = (\frac{3 - ((3 + (6 - 1) \cdot 4) \cdot 2^{6})}{1 - 2}) + (4 \cdot 2 \cdot \frac{1 - 2^{6 - 1}}{{(1 - 2)}^{2}})

1221 = (\frac{3 - ((3 + (6 - 1) \cdot 4) \cdot 2^{6})}{1 - 2}) + (4 \cdot 2 \cdot \frac{1 - 2^{6 - 1}}{{(1 - 2)}^{2}})

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Sum of First N Terms of Arithmetic Geometric Progression Solution

Follow our step by step solution on how to calculate Sum of First N Terms of Arithmetic Geometric Progression?

FIRST Step Consider the formula

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}})

Next Step Substitute values of Variables

∴

S n = (\frac{3 - ((3 + (6 - 1) \cdot 4) \cdot 2^{6})}{1 - 2}) + (4 \cdot 2 \cdot \frac{1 - 2^{6 - 1}}{{(1 - 2)}^{2}})

Next Step Prepare to Evaluate

∴

S n = (\frac{3 - ((3 + (6 - 1) \cdot 4) \cdot 2^{6})}{1 - 2}) + (4 \cdot 2 \cdot \frac{1 - 2^{6 - 1}}{{(1 - 2)}^{2}})

LAST Step Evaluate

∴

S n = 1221

Sum of First N Terms of Arithmetic Geometric Progression Formula Elements

Variables

Sum of First N Terms of Progression

The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression.

Symbol: S_n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Sum of First N Terms of 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

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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Index N of 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

Common Ratio of Progression

The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Common Ratio 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 Infinite Arithmetic Geometric Progression

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

How to Evaluate Sum of First N Terms of Arithmetic Geometric Progression?

Sum of First N Terms of Arithmetic Geometric Progression evaluator uses 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) to evaluate the Sum of First N Terms of Progression, The Sum of First N Terms of Arithmetic Geometric Progression formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Geometric Progression. Sum of First N Terms of Progression is denoted by S_n symbol.

How to evaluate Sum of First N Terms of Arithmetic Geometric Progression using this online evaluator? To use this online evaluator for Sum of First N Terms of Arithmetic Geometric Progression, enter First Term of Progression (a), Index N of Progression (n), Common Difference of Progression (d) & Common Ratio of Progression (r) and hit the calculate button.

FAQs on Sum of First N Terms of Arithmetic Geometric Progression

What is the formula to find Sum of First N Terms of Arithmetic Geometric Progression?

The formula of Sum of First N Terms of Arithmetic Geometric Progression is expressed as 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). Here is an example- 1221 = ((3-((3+(6-1)*4)*2^(6)))/(1-2))+(4*2*(1-2^(6-1))/(1-2)^2).

How to calculate Sum of First N Terms of Arithmetic Geometric Progression?

With First Term of Progression (a), Index N of Progression (n), Common Difference of Progression (d) & Common Ratio of Progression (r) we can find Sum of First N Terms of Arithmetic Geometric Progression using the formula - 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).

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Sum of First N Terms of Arithmetic Geometric Progression Formula

Sum of First N Terms of Arithmetic Geometric Progression Example

Sum of First N Terms of Arithmetic Geometric Progression Solution

Sum of First N Terms of Arithmetic Geometric Progression Formula Elements

Other formulas in Arithmetic Geometric Progression category

How to Evaluate Sum of First N Terms of Arithmetic Geometric Progression?

FAQs on Sum of First N Terms of Arithmetic Geometric Progression

Variable Name