Last Term of Arithmetic Progression given Pth and Qth Terms Calculator

✖The Pth Term of Progression is the term corresponding to the index or position p from the beginning of the given Progression.ⓘ Pth Term of Progression [T_p]			+10% -10%
✖The Index Q of Progression is the value of q for the qth term or the position of the qth term in the Progression.ⓘ Index Q of Progression [q]			+10% -10%
✖The Qth Term of Progression is the term corresponding to the index or position q from the beginning of the given Progression.ⓘ Qth Term of Progression [T_q]			+10% -10%
✖The Index P of Progression is the value of p for the pth term or the position of the pth term in the Progression.ⓘ Index P of Progression [p]			+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 Last Term of Progression is the term at which the given Progression terminates.ⓘ Last Term of Arithmetic Progression given Pth and Qth Terms [l]

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Formula

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Last Term of Arithmetic Progression given Pth and Qth Terms

Formula

`"l" = (("T"_{"p"}*("q"-1)-"T"_{"q"}*("p"-1))/("q"-"p"))+("n"_{"Total"}-1)*(("T"_{"q"}-"T"_{"p"})/("q"-"p"))`

Example

`"100"=(("50"*("8"-1)-"80"*("5"-1))/("8"-"5"))+("10"-1)*(("80"-"50")/("8"-"5"))`

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Last Term of Arithmetic Progression given Pth and Qth Terms Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
l = ((T_p*(q-1)-T_q*(p-1))/(q-p))+(n_Total-1)*((T_q-T_p)/(q-p))
This formula uses 6 Variables

Variables Used

Last Term of Progression - The Last Term of Progression is the term at which the given Progression terminates.
Pth Term of Progression - The Pth Term of Progression is the term corresponding to the index or position p from the beginning of the given Progression.
Index Q of Progression - The Index Q of Progression is the value of q for the qth term or the position of the qth term in the Progression.
Qth Term of Progression - The Qth Term of Progression is the term corresponding to the index or position q from the beginning of the given Progression.
Index P of Progression - The Index P of Progression is the value of p for the pth term or the position of the pth term in the 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.

STEP 1: Convert Input(s) to Base Unit

Pth Term of Progression: 50 --> No Conversion Required
Index Q of Progression: 8 --> No Conversion Required
Qth Term of Progression: 80 --> No Conversion Required
Index P of Progression: 5 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = ((T_p*(q-1)-T_q*(p-1))/(q-p))+(n_Total-1)*((T_q-T_p)/(q-p)) --> ((50*(8-1)-80*(5-1))/(8-5))+(10-1)*((80-50)/(8-5))

Evaluating ... ...

l = 100

STEP 3: Convert Result to Output's Unit

100 --> No Conversion Required

FINAL ANSWER

100 <-- Last Term of Progression

(Calculation completed in 00.004 seconds)

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< 5 Last Term of Arithmetic Progression Calculators

Last Term of Arithmetic Progression given Pth and Qth Terms

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 Nth Term

Go Last Term of Progression = First Term of Progression+(Number of Total Terms of Progression-1)*((Nth Term of Progression-First Term of Progression)/(Index N of Progression-1))

Last Term of Arithmetic Progression given Sum of Last N Terms

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

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

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 Pth and Qth Terms Formula

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 Pth and Qth Terms?

Last Term of Arithmetic Progression given Pth and Qth Terms calculator uses 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)) to calculate the Last Term of Progression, The Last Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the pth and qth terms of the Arithmetic Progression. Last Term of Progression is denoted by l symbol.

How to calculate Last Term of Arithmetic Progression given Pth and Qth Terms using this online calculator? To use this online calculator for Last Term of Arithmetic Progression given Pth and Qth Terms, enter Pth Term of Progression (T_p), Index Q of Progression (q), Qth Term of Progression (T_q), Index P of Progression (p) & Number of Total Terms of Progression (n_Total) and hit the calculate button. Here is how the Last Term of Arithmetic Progression given Pth and Qth Terms calculation can be explained with given input values -> -5 = ((50*(8-1)-80*(5-1))/(8-5))+(10-1)*((80-50)/(8-5)).

FAQ

What is Last Term of Arithmetic Progression given Pth and Qth Terms?

The Last Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the pth and qth terms of the Arithmetic Progression and is represented as l = ((T_p*(q-1)-T_q*(p-1))/(q-p))+(n_Total-1)*((T_q-T_p)/(q-p)) or 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)). The Pth Term of Progression is the term corresponding to the index or position p from the beginning of the given Progression, The Index Q of Progression is the value of q for the qth term or the position of the qth term in the Progression, The Qth Term of Progression is the term corresponding to the index or position q from the beginning of the given Progression, The Index P of Progression is the value of p for the pth term or the position of the pth term in the Progression & The Number of Total Terms of Progression is the total number of terms present in the given sequence of Progression.

How to calculate Last Term of Arithmetic Progression given Pth and Qth Terms?

The Last Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the pth and qth terms of the Arithmetic Progression is calculated using 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)). To calculate Last Term of Arithmetic Progression given Pth and Qth Terms, you need Pth Term of Progression (T_p), Index Q of Progression (q), Qth Term of Progression (T_q), Index P of Progression (p) & Number of Total Terms of Progression (n_Total). With our tool, you need to enter the respective value for Pth Term of Progression, Index Q of Progression, Qth Term of Progression, Index P 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 Last Term of Progression?

In this formula, Last Term of Progression uses Pth Term of Progression, Index Q of Progression, Qth Term of Progression, Index P of Progression & Number of Total Terms of Progression. We can use 4 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 = ((2*Sum of Total Terms of Progression)/Number of Total Terms of Progression)-First Term of Progression
Last Term of Progression = First Term of Progression+(Number of Total Terms of Progression-1)*((Nth Term of Progression-First Term of Progression)/(Index N of Progression-1))

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