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The Last Term of Progression is the term at which the given Progression terminates. Check FAQs
l=(Sn(End)n-d⋅(1-n)2)
l - Last Term of Progression?Sn(End) - Sum of Last N Terms of Progression?n - Index N of Progression?d - Common Difference of Progression?

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

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Here is how the Last Term of Arithmetic Progression given Sum of Last N Terms equation looks like with Values.

Here is how the Last Term of Arithmetic Progression given Sum of Last N Terms equation looks like with Units.

Here is how the Last Term of Arithmetic Progression given Sum of Last N Terms equation looks like.

143.3333Edit=(800Edit6Edit-4Edit⋅(1-6Edit)2)
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Last Term of Arithmetic Progression given Sum of Last N Terms Solution

Follow our step by step solution on how to calculate Last Term of Arithmetic Progression given Sum of Last N Terms?

FIRST Step Consider the formula
l=(Sn(End)n-d⋅(1-n)2)
Next Step Substitute values of Variables
∴ l=(8006-4⋅(1-6)2)
Next Step Prepare to Evaluate
∴ l=(8006-4⋅(1-6)2)
Next Step Evaluate
∴l=143.333333333333
LAST Step Rounding Answer
∴l=143.3333

Last Term of Arithmetic Progression given Sum of Last N Terms Formula Elements

Variables
Last Term of Progression
The Last Term of Progression is the term at which the given Progression terminates.
Symbol: l
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Last Term of ProgressionOpen Variable
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.
Symbol: Sn(End)
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Sum of Last N Terms of ProgressionOpen Variable
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.
Symbol: n
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Index N of ProgressionOpen Variable
Common Difference of Progression
The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.
Symbol: d
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Common Difference of ProgressionOpen Variable

Credits

Creator Image
Created by Nayana Phulphagar LinkedIn Logo
Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI
Nayana Phulphagar has created this Formula and 300+ more formulas!
Verifier Image
Verified by Nikita Salampuria LinkedIn Logo
The National Institute of Engineering (NIE), Mysuru
Nikita Salampuria has verified this Formula and 600+ more formulas!

Other Formulas to find Last Term of Progression

​Go Last Term of Arithmetic Progression
l=a+((nTotal-1)⋅d)
​Go Last Term of Arithmetic Progression given Pth and Qth Terms
l=(Tp⋅(q-1)-Tq⋅(p-1)q-p)+(nTotal-1)⋅(Tq-Tpq-p)
​Go Last Term of Arithmetic Progression given Sum of Total Terms
l=(2⋅STotalnTotal)-a
​Go Last Term of Arithmetic Progression given Nth Term
l=a+(nTotal-1)⋅(Tn-an-1)

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

Last Term of Arithmetic Progression given Sum of Last N Terms evaluator uses Last Term of Progression = (Sum of Last N Terms of Progression/Index N of Progression-(Common Difference of Progression*(1-Index N of Progression))/2) to evaluate the Last Term of Progression, The Last Term of Arithmetic Progression given Sum of Last N Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the sum of the last n terms of the Arithmetic Progression. Last Term of Progression is denoted by l symbol.

How to evaluate Last Term of Arithmetic Progression given Sum of Last N Terms using this online evaluator? To use this online evaluator for Last Term of Arithmetic Progression given Sum of Last N Terms, enter Sum of Last N Terms of Progression (Sn(End)), Index N of Progression (n) & Common Difference of Progression (d) and hit the calculate button.

FAQs on Last Term of Arithmetic Progression given Sum of Last N Terms

What is the formula to find Last Term of Arithmetic Progression given Sum of Last N Terms?
The formula of Last Term of Arithmetic Progression given Sum of Last N Terms is expressed as Last Term of Progression = (Sum of Last N Terms of Progression/Index N of Progression-(Common Difference of Progression*(1-Index N of Progression))/2). Here is an example- 36.66667 = (800/6-(4*(1-6))/2).
How to calculate Last Term of Arithmetic Progression given Sum of Last N Terms?
With Sum of Last N Terms of Progression (Sn(End)), Index N of Progression (n) & Common Difference of Progression (d) we can find Last Term of Arithmetic Progression given Sum of Last N Terms using the formula - Last Term of Progression = (Sum of Last N Terms of Progression/Index N of Progression-(Common Difference of Progression*(1-Index N of Progression))/2).
What are the other ways to Calculate Last Term of Progression?
Here are the different ways to Calculate Last Term of Progression-
  • Last Term of Progression=First Term of Progression+((Number of Total Terms of Progression-1)*Common Difference of Progression)OpenImg
  • Last Term of Progression=((Pth Term of Progression*(Index Q of Progression-1)-Qth Term of Progression*(Index P of Progression-1))/(Index Q of Progression-Index P of Progression))+(Number of Total Terms of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))OpenImg
  • Last Term of Progression=((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of ProgressionOpenImg
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