Sum of Last N Terms of Arithmetic Progression Calculator

✖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 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 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 Sum of Last N Terms of Progression is the summation of the terms starting from the end to the nth term of a given Progression.ⓘ Sum of Last N Terms of Arithmetic Progression [S_n(End)]

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Sum of Last N Terms of Arithmetic Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Sum of Last N Terms of Progression - The Sum of Last N Terms of Progression is the summation of the terms starting from the end to the nth term of a given 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Index N of Progression: 6 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n(End) = (n/2)*((2*a)+(d*((2*n_Total)-n-1))) --> (6/2)*((2*3)+(4*((2*10)-6-1)))

Evaluating ... ...

S_n(End) = 174

STEP 3: Convert Result to Output's Unit

174 --> No Conversion Required

FINAL ANSWER

174 <-- Sum of Last N 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 Last N 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 Last N Terms of Arithmetic Progression?

Sum of Last N Terms of Arithmetic Progression calculator uses 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))) to calculate the Sum of Last N Terms of Progression, The Sum of Last N Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression. Sum of Last N Terms of Progression is denoted by S_n(End) symbol.

How to calculate Sum of Last N Terms of Arithmetic Progression using this online calculator? To use this online calculator for Sum of Last N Terms of Arithmetic Progression, enter Index N of Progression (n), First Term of Progression (a), Common Difference of Progression (d) & Number of Total Terms of Progression (n_Total) and hit the calculate button. Here is how the Sum of Last N Terms of Arithmetic Progression calculation can be explained with given input values -> 174 = (6/2)*((2*3)+(4*((2*10)-6-1))).

FAQ

What is Sum of Last N Terms of Arithmetic Progression?

The Sum of Last N Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression and is represented as S_n(End) = (n/2)*((2*a)+(d*((2*n_Total)-n-1))) or 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))). 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 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 & The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.

How to calculate Sum of Last N Terms of Arithmetic Progression?

The Sum of Last N Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression is calculated using 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))). To calculate Sum of Last N Terms of Arithmetic Progression, you need Index N of Progression (n), First Term of Progression (a), Common Difference of Progression (d) & Number of Total Terms of Progression (n_Total). With our tool, you need to enter the respective value for Index N of Progression, First Term of Progression, Common Difference of Progression & Number of Total Terms 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 Last N Terms of Progression?

In this formula, Sum of Last N Terms of Progression uses Index N of Progression, First Term of Progression, Common Difference of Progression & Number of Total Terms of Progression. We can use 2 other way(s) to calculate the same, which is/are as follows -

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 Last N Terms of Progression = (Index N of Progression/2)*(Last Term of Progression+Nth Term from End of Progression)

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