Sum of Total Terms of Arithmetic Progression given Last Term 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 Last Term of Progression is the term at which the given Progression terminates.ⓘ Last Term of Progression [l]			+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 given Last Term [S_Total]

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Sum of Total Terms of Arithmetic Progression given Last Term Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression)
S_Total = (n_Total/2)*(a+l)
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.
Last Term of Progression - The Last Term of Progression is the term at which the given Progression terminates.

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
Last Term of Progression: 100 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_Total = (n_Total/2)*(a+l) --> (10/2)*(3+100)

Evaluating ... ...

S_Total = 515

STEP 3: Convert Result to Output's Unit

515 --> No Conversion Required

FINAL ANSWER

515 <-- Sum of Total Terms of Progression

(Calculation completed in 00.004 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)

< Arithmetic Progression Calculators

Sum of First N Terms of Arithmetic Progression

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

Nth Term of Arithmetic Progression

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

Common Difference of Arithmetic Progression

LaTeX Go Common Difference of Progression = Nth Term of Progression-(N-1)th Term of Progression

Sum of Total Terms of Arithmetic Progression given Last Term Formula

LaTeX Go

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

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 given Last Term?

Sum of Total Terms of Arithmetic Progression given Last Term calculator uses Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression) to calculate the Sum of Total Terms of Progression, The Sum of Total Terms of Arithmetic Progression given Last Term formula is defined as the summation of the terms starting from the first to the last term of given Arithmetic Progression, and is calculated using the last term of the 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 given Last Term using this online calculator? To use this online calculator for Sum of Total Terms of Arithmetic Progression given Last Term, enter Number of Total Terms of Progression (n_Total), First Term of Progression (a) & Last Term of Progression (l) and hit the calculate button. Here is how the Sum of Total Terms of Arithmetic Progression given Last Term calculation can be explained with given input values -> 515 = (10/2)*(3+100).

FAQ

What is Sum of Total Terms of Arithmetic Progression given Last Term?

The Sum of Total Terms of Arithmetic Progression given Last Term formula is defined as the summation of the terms starting from the first to the last term of given Arithmetic Progression, and is calculated using the last term of the given Arithmetic Progression and is represented as S_Total = (n_Total/2)*(a+l) or Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term 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 Last Term of Progression is the term at which the given Progression terminates.

How to calculate Sum of Total Terms of Arithmetic Progression given Last Term?

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

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