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Sum of First N Terms of 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 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 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 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 Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression.ⓘ Sum of First N Terms of Arithmetic Geometric Progression [S_n]

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Sum of First N Terms of Arithmetic Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
S_n = ((a-((a+(n-1)*d)*r^(n)))/(1-r))+(d*r*(1-r^(n-1))/(1-r)^2)
This formula uses 5 Variables

Variables Used

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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
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.
Common Difference of Progression - The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.
Common Ratio of Progression - The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.

STEP 1: Convert Input(s) to Base Unit

First Term of Progression: 3 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required
Common Ratio of Progression: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n = ((a-((a+(n-1)*d)*r^(n)))/(1-r))+(d*r*(1-r^(n-1))/(1-r)^2) --> ((3-((3+(6-1)*4)*2^(6)))/(1-2))+(4*2*(1-2^(6-1))/(1-2)^2)

Evaluating ... ...

S_n = 1221

STEP 3: Convert Result to Output's Unit

1221 --> No Conversion Required

FINAL ANSWER

1221 <-- Sum of First N Terms of Progression

(Calculation completed in 00.004 seconds)

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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 First N Terms of 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 First N Terms of Arithmetic Geometric Progression?

Sum of First N Terms of Arithmetic Geometric Progression calculator 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 calculate 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 calculate Sum of First N Terms of Arithmetic Geometric Progression using this online calculator? To use this online calculator 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. Here is how the Sum of First N Terms of Arithmetic Geometric Progression calculation can be explained with given input values -> 1221 = ((3-((3+(6-1)*4)*2^(6)))/(1-2))+(4*2*(1-2^(6-1))/(1-2)^2).

FAQ

What is Sum of First N Terms of Arithmetic Geometric 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 and is represented as S_n = ((a-((a+(n-1)*d)*r^(n)))/(1-r))+(d*r*(1-r^(n-1))/(1-r)^2) or 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). The First Term of Progression is the term at which the given Progression starts, The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression, The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant & The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.

How to calculate Sum of First N Terms of Arithmetic Geometric 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 is calculated using 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 calculate Sum of First N Terms of Arithmetic Geometric Progression, you need First Term of Progression (a), Index N of Progression (n), Common Difference of Progression (d) & Common Ratio of Progression (r). With our tool, you need to enter the respective value for First Term of Progression, Index N of Progression, Common Difference of Progression & Common Ratio 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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