Sum of Total Terms of Arithmetic Progression Calculator

✖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 First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+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 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 Arithmetic Progression [S_Total]

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Sum of Total Terms of Arithmetic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*((2*First Term of Progression)+((Number of Total Terms of Progression-1)*Common Difference of Progression))
S_Total = (n_Total/2)*((2*a)+((n_Total-1)*d))
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.
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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
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

Number of Total Terms of Progression: 10 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_Total = (n_Total/2)*((2*a)+((n_Total-1)*d)) --> (10/2)*((2*3)+((10-1)*4))

Evaluating ... ...

S_Total = 210

STEP 3: Convert Result to Output's Unit

210 --> No Conversion Required

FINAL ANSWER

210 <-- Sum of Total Terms of Progression

(Calculation completed in 00.020 seconds)

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< Sum of Terms of Arithmetic Progression Calculators

Sum of Last N Terms of Arithmetic Progression

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

Sum of Total Terms of Arithmetic Progression

LaTeX Go Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*((2*First Term of Progression)+((Number of Total Terms of Progression-1)*Common Difference of Progression))

Sum of Last N Terms of Arithmetic Progression given Last Term

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

Sum of Total Terms of Arithmetic Progression given Last Term

LaTeX Go Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression)

Sum of Total Terms of Arithmetic Progression Formula

LaTeX Go

What is an Arithmetic Progression?

An Arithmetic Progression or simply AP is a sequence of numbers such that successive terms are obtained by adding a constant number to the first term. That fixed number is called the common difference of the Arithmetic Progression. For example, the sequence 2, 5, 8, 11, 14,... is an Arithmetic Progression with first term is 2 and common difference is 3. An AP is a convergent sequence if and only if the common difference is 0, otherwise an AP is always divergent.

How to Calculate Sum of Total Terms of Arithmetic Progression?

Sum of Total Terms of Arithmetic Progression calculator uses Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*((2*First Term of Progression)+((Number of Total Terms of Progression-1)*Common Difference of Progression)) to calculate the Sum of Total Terms of Progression, The Sum of Total Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the first to the last term of given Arithmetic Progression. Sum of Total Terms of Progression is denoted by S_Total symbol.

How to calculate Sum of Total Terms of Arithmetic Progression using this online calculator? To use this online calculator for Sum of Total Terms of Arithmetic Progression, enter Number of Total Terms of Progression (n_Total), First Term of Progression (a) & Common Difference of Progression (d) and hit the calculate button. Here is how the Sum of Total Terms of Arithmetic Progression calculation can be explained with given input values -> 210 = (10/2)*((2*3)+((10-1)*4)).

FAQ

What is Sum of Total Terms of Arithmetic Progression?

The Sum of Total Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the first to the last term of given Arithmetic Progression and is represented as S_Total = (n_Total/2)*((2*a)+((n_Total-1)*d)) or Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*((2*First Term of Progression)+((Number of Total Terms of Progression-1)*Common Difference of Progression)). The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression, The First Term of Progression is the term at which the given Progression starts & 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 Total Terms of Arithmetic Progression?

The Sum of Total Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the first to the last term of given Arithmetic Progression is calculated using Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*((2*First Term of Progression)+((Number of Total Terms of Progression-1)*Common Difference of Progression)). To calculate Sum of Total Terms of Arithmetic Progression, you need Number of Total Terms of Progression (n_Total), First Term of Progression (a) & Common Difference of Progression (d). With our tool, you need to enter the respective value for Number of Total Terms of Progression, First Term of 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.

How many ways are there to calculate Sum of Total Terms of Progression?

In this formula, Sum of Total Terms of Progression uses Number of Total Terms of Progression, First Term of Progression & Common Difference of Progression. We can use 1 other way(s) to calculate the same, which is/are as follows -

Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression)

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