Sum of Last N Terms of Arithmetic Progression given Last Term 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 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 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 Last Term [S_n(End)]

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Sum of Last N Terms of Arithmetic Progression given Last Term Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
S_n(End) = (n/2)*((2*l)+(d*(1-n)))
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.
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

Index N of Progression: 6 --> No Conversion Required
Last Term of Progression: 100 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n(End) = (n/2)*((2*l)+(d*(1-n))) --> (6/2)*((2*100)+(4*(1-6)))

Evaluating ... ...

S_n(End) = 540

STEP 3: Convert Result to Output's Unit

540 --> No Conversion Required

FINAL ANSWER

540 <-- Sum of Last N 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 Last N Terms of Arithmetic Progression given Last Term Formula

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)))
S_n(End) = (n/2)*((2*l)+(d*(1-n)))

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 Last Term?

Sum of Last N Terms of Arithmetic Progression given Last Term calculator uses 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))) to calculate the Sum of Last N Terms of Progression, The Sum of Last N Terms of Arithmetic Progression given Last Term formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression, and calculated using last term 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 Last Term using this online calculator? To use this online calculator for Sum of Last N Terms of Arithmetic Progression given Last Term, enter Index N of Progression (n), Last Term of Progression (l) & Common Difference of Progression (d) and hit the calculate button. Here is how the Sum of Last N Terms of Arithmetic Progression given Last Term calculation can be explained with given input values -> 540 = (6/2)*((2*100)+(4*(1-6))).

FAQ

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

The Sum of Last N Terms of Arithmetic Progression given Last Term formula is defined as the summation of the terms starting from the end to the nth term of given Arithmetic Progression, and calculated using last term of Arithmetic Progression and is represented as S_n(End) = (n/2)*((2*l)+(d*(1-n))) or 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))). 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 Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

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

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

In this formula, Sum of Last N Terms of Progression uses Index N of Progression, Last Term of Progression & Common Difference 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*First Term of Progression)+(Common Difference of Progression*((2*Number of Total Terms of Progression)-Index N of Progression-1)))
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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