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))
Tn = ((Tp*(q-1)-Tq*(p-1))/(q-p))+(n-1)*((Tq-Tp)/(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
Tn = ((Tp*(q-1)-Tq*(p-1))/(q-p))+(n-1)*((Tq-Tp)/(q-p)) --> ((50*(8-1)-80*(5-1))/(8-5))+(6-1)*((80-50)/(8-5))
Evaluating ... ...
Tn = 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)

Credits

Created by Mayank Tayal
National Institute of Technology (NIT), Durgapur
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6 Nth Term of Arithmetic Progression Calculators

Nth Term of Arithmetic Progression given Pth and Qth Terms
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 of Arithmetic Progression given Last Term
Go 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))
Nth Term from End of Arithmetic Progression
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 from End of Arithmetic Progression given Last Term
Go Nth Term from End of Progression = Last Term of Progression-(Index N of Progression-1)*Common Difference of Progression
Nth Term of Arithmetic Progression given Sum of First N Terms
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
Go Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression

11 Arithmetic Progression Calculators

Nth Term of Arithmetic Progression given Pth and Qth Terms
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))
Sum of Terms from Pth to Qth Terms of Arithmetic Progression
Go Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression))
Sum of Last N Terms of Arithmetic Progression
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 First N Terms of Arithmetic Progression
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))
Nth Term from End of Arithmetic Progression
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
Common Difference of Arithmetic Progression given Last Term
Go Common Difference of Progression = ((Last Term of Progression-First Term of Progression)/(Number of Total Terms of Progression-1))
Sum of Total Terms of Arithmetic Progression given Last Term
Go Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression)
Number of Terms of Arithmetic Progression
Go Index N of Progression = ((Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1
First Term of Arithmetic Progression
Go First Term of Progression = Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)
Nth Term of Arithmetic Progression
Go Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
Common Difference of Arithmetic Progression
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

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))
Tn = ((Tp*(q-1)-Tq*(p-1))/(q-p))+(n-1)*((Tq-Tp)/(q-p))

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 Tn 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 (Tp), Index Q of Progression (q), Qth Term of Progression (Tq), 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 Tn = ((Tp*(q-1)-Tq*(p-1))/(q-p))+(n-1)*((Tq-Tp)/(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 (Tp), Index Q of Progression (q), Qth Term of Progression (Tq), 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 4 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))
  • Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
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