Last Term of Arithmetic Progression given Sum of Total Terms Solution

STEP 0: Pre-Calculation Summary
Formula Used
Last Term of Progression = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of Progression
l = ((2*STotal)/nTotal)-a
This formula uses 4 Variables
Variables Used
Last Term of Progression - The Last Term of Progression is the term at which the given Progression terminates.
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.
STEP 1: Convert Input(s) to Base Unit
Sum of Total Terms of Progression: 1000 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = ((2*STotal)/nTotal)-a --> ((2*1000)/10)-3
Evaluating ... ...
l = 197
STEP 3: Convert Result to Output's Unit
197 --> No Conversion Required
FINAL ANSWER
197 <-- Last Term of Progression
(Calculation completed in 00.020 seconds)

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Last Term of Arithmetic Progression Calculators

Last Term of Arithmetic Progression given Pth and Qth Terms
​ LaTeX ​ Go 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))
Last Term of Arithmetic Progression given Sum of Last N Terms
​ LaTeX ​ Go 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)
Last Term of Arithmetic Progression given Sum of Total Terms
​ LaTeX ​ Go Last Term of Progression = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of Progression
Last Term of Arithmetic Progression
​ LaTeX ​ Go Last Term of Progression = First Term of Progression+((Number of Total Terms of Progression-1)*Common Difference of Progression)

Last Term of Arithmetic Progression given Sum of Total Terms Formula

​LaTeX ​Go
Last Term of Progression = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of Progression
l = ((2*STotal)/nTotal)-a

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 Last Term of Arithmetic Progression given Sum of Total Terms?

Last Term of Arithmetic Progression given Sum of Total Terms calculator uses Last Term of Progression = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of Progression to calculate the Last Term of Progression, The Last Term of Arithmetic Progression given Sum of Total Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the sum of total terms of given Arithmetic Progression. Last Term of Progression is denoted by l symbol.

How to calculate Last Term of Arithmetic Progression given Sum of Total Terms using this online calculator? To use this online calculator for Last Term of Arithmetic Progression given Sum of Total Terms, enter Sum of Total Terms of Progression (STotal), Number of Total Terms of Progression (nTotal) & First Term of Progression (a) and hit the calculate button. Here is how the Last Term of Arithmetic Progression given Sum of Total Terms calculation can be explained with given input values -> 150 = ((2*1000)/10)-3.

FAQ

What is Last Term of Arithmetic Progression given Sum of Total Terms?
The Last Term of Arithmetic Progression given Sum of Total Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the sum of total terms of given Arithmetic Progression and is represented as l = ((2*STotal)/nTotal)-a or Last Term of Progression = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term 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, 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.
How to calculate Last Term of Arithmetic Progression given Sum of Total Terms?
The Last Term of Arithmetic Progression given Sum of Total Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the sum of total terms of given Arithmetic Progression is calculated using Last Term of Progression = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of Progression. To calculate Last Term of Arithmetic Progression given Sum of Total Terms, you need Sum of Total Terms of Progression (STotal), Number of Total Terms of Progression (nTotal) & First Term of Progression (a). With our tool, you need to enter the respective value for Sum of Total Terms of Progression, Number of Total Terms of Progression & First 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 Last Term of Progression?
In this formula, Last Term of Progression uses Sum of Total Terms of Progression, Number of Total Terms of Progression & First Term of Progression. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Last Term of Progression = First Term of Progression+((Number of Total Terms of Progression-1)*Common Difference of Progression)
  • 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)
  • 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))
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