Nth 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 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 Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.ⓘ Nth Term of Arithmetic Progression given Pth and Qth Terms [T_n]

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Nth Term of Arithmetic Progression given Pth and Qth Terms Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth 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))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))
T_n = ((T_p*(q-1)-T_q*(p-1))/(q-p))+(n-1)*((T_q-T_p)/(q-p))
This formula uses 6 Variables

Variables Used

Nth Term of Progression - The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.
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.
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.

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
Index N of Progression: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = ((T_p*(q-1)-T_q*(p-1))/(q-p))+(n-1)*((T_q-T_p)/(q-p)) --> ((50*(8-1)-80*(5-1))/(8-5))+(6-1)*((80-50)/(8-5))

Evaluating ... ...

T_n = 60

STEP 3: Convert Result to Output's Unit

60 --> No Conversion Required

FINAL ANSWER

60 <-- Nth Term of Progression

(Calculation completed in 00.004 seconds)

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< Nth Term of Arithmetic Progression Calculators

Nth Term of Arithmetic Progression given Pth and Qth Terms

LaTeX Go Nth 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))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))

Nth Term from End of Arithmetic Progression

LaTeX Go Nth Term from End of Progression = First Term of Progression+(Number of Total Terms of Progression-Index N of Progression)*Common Difference of Progression

Nth Term of Arithmetic Progression given Sum of First N Terms

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

Nth Term of Arithmetic Progression

LaTeX Go Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression

< Arithmetic Progression Calculators

Sum of First N Terms of Arithmetic Progression

LaTeX 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 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)

Nth Term of Arithmetic Progression

LaTeX Go Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression

Common Difference of Arithmetic Progression

LaTeX Go Common Difference of Progression = Nth Term of Progression-(N-1)th Term of Progression

Nth Term of Arithmetic Progression given Pth and Qth Terms Formula

LaTeX Go

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 Nth Term of Arithmetic Progression given Pth and Qth Terms?

Nth Term of Arithmetic Progression given Pth and Qth Terms calculator uses Nth 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))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)) to calculate the Nth Term of Progression, The Nth Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the pth and qth terms of the Arithmetic Progression. Nth Term of Progression is denoted by T_n symbol.

How to calculate Nth Term of Arithmetic Progression given Pth and Qth Terms using this online calculator? To use this online calculator for Nth 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) & Index N of Progression (n) and hit the calculate button. Here is how the Nth Term of Arithmetic Progression given Pth and Qth Terms calculation can be explained with given input values -> 39 = ((50*(8-1)-80*(5-1))/(8-5))+(6-1)*((80-50)/(8-5)).

FAQ

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

The Nth Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the pth and qth terms of the Arithmetic Progression and is represented as T_n = ((T_p*(q-1)-T_q*(p-1))/(q-p))+(n-1)*((T_q-T_p)/(q-p)) or Nth 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))+(Index N 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 Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.

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

The Nth Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the pth and qth terms of the Arithmetic Progression is calculated using Nth 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))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)). To calculate Nth 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) & Index N of Progression (n). 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 & Index N 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 Nth Term of Progression?

In this formula, Nth Term of Progression uses Pth Term of Progression, Index Q of Progression, Qth Term of Progression, Index P of Progression & Index N of Progression. We can use 3 other way(s) to calculate the same, which is/are as follows -

Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression
Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*((Last Term of Progression-First Term of Progression)/(Number of Total Terms of Progression-1))

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