Sum of Last N Terms of Arithmetic Progression given Nth Term from End 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 Last Term of Progression is the term at which the given Progression terminates.ⓘ Last Term of Progression [l]			+10% -10%
✖The Nth Term from End of Progression is the term corresponding to the index or position n from the end of the given Progression.ⓘ Nth Term from End of Progression [T_n(End)]			+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 given Nth Term from End [S_n(End)]

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Formula

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Sum of Last N Terms of Arithmetic Progression given Nth Term from End

Formula

`"S"_{"n(End)"} = ("n"/2)*("l"+"T"_{"n(End)"})`

Example

`"420"=("6"/2)*("100"+"40")`

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Sum of Last N Terms of Arithmetic Progression given Nth Term from End Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Last N Terms of Progression = (Index N of Progression/2)*(Last Term of Progression+Nth Term from End of Progression)
S_n(End) = (n/2)*(l+T_n(End))
This formula uses 4 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.
Last Term of Progression - The Last Term of Progression is the term at which the given Progression terminates.
Nth Term from End of Progression - The Nth Term from End of Progression is the term corresponding to the index or position n from the end of the given Progression.

STEP 1: Convert Input(s) to Base Unit

Index N of Progression: 6 --> No Conversion Required
Last Term of Progression: 100 --> No Conversion Required
Nth Term from End of Progression: 40 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n(End) = (n/2)*(l+T_n(End)) --> (6/2)*(100+40)

Evaluating ... ...

S_n(End) = 420

STEP 3: Convert Result to Output's Unit

420 --> No Conversion Required

FINAL ANSWER

420 <-- Sum of Last N Terms of Progression

(Calculation completed in 00.020 seconds)

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< 8 Sum of Terms of Arithmetic Progression Calculators

Sum of Terms from Pth to Qth Terms of Arithmetic Progression

Go Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression))

Sum of Last N Terms of Arithmetic Progression

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

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 First N Terms of Arithmetic Progression

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 Last N Terms of Arithmetic Progression given Last Term

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

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

Sum of Last N Terms of Arithmetic Progression given Nth Term from End

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

Sum of First N Terms of Arithmetic Progression given NthTerm

Go Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression)

Sum of Last N Terms of Arithmetic Progression given Nth Term from End Formula

Sum of Last N Terms of Progression = (Index N of Progression/2)*(Last Term of Progression+Nth Term from End of Progression)
S_n(End) = (n/2)*(l+T_n(End))

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 given Nth Term from End?

Sum of Last N Terms of Arithmetic Progression given Nth Term from End calculator uses Sum of Last N Terms of Progression = (Index N of Progression/2)*(Last Term of Progression+Nth Term from End of Progression) to calculate the Sum of Last N Terms of Progression, The Sum of Last N Terms of Arithmetic Progression given Nth Term from End formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression, and calculated using the nth term from end of 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 given Nth Term from End using this online calculator? To use this online calculator for Sum of Last N Terms of Arithmetic Progression given Nth Term from End, enter Index N of Progression (n), Last Term of Progression (l) & Nth Term from End of Progression (T_n(End)) and hit the calculate button. Here is how the Sum of Last N Terms of Arithmetic Progression given Nth Term from End calculation can be explained with given input values -> 420 = (6/2)*(100+40).

FAQ

What is Sum of Last N Terms of Arithmetic Progression given Nth Term from End?

The Sum of Last N Terms of Arithmetic Progression given Nth Term from End formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression, and calculated using the nth term from end of Arithmetic Progression and is represented as S_n(End) = (n/2)*(l+T_n(End)) or Sum of Last N Terms of Progression = (Index N of Progression/2)*(Last Term of Progression+Nth Term from End 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, The Last Term of Progression is the term at which the given Progression terminates & The Nth Term from End of Progression is the term corresponding to the index or position n from the end of the given Progression.

How to calculate Sum of Last N Terms of Arithmetic Progression given Nth Term from End?

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

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