Nth Term of Arithmetic Progression Solution

STEP 0: Pre-Calculation Summary
Formula Used
Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
Tn = a+(n-1)*d
This formula uses 4 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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
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.
Common Difference of Progression - The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.
STEP 1: Convert Input(s) to Base Unit
First Term of Progression: 3 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tn = a+(n-1)*d --> 3+(6-1)*4
Evaluating ... ...
Tn = 23
STEP 3: Convert Result to Output's Unit
23 --> No Conversion Required
FINAL ANSWER
23 <-- Nth Term of Progression
(Calculation completed in 00.004 seconds)

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Indian Institute of Information Technology (IIIT), Bhopal
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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 Formula

Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
Tn = a+(n-1)*d

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?

Nth Term of Arithmetic Progression calculator uses Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression to calculate the Nth Term of Progression, The Nth Term of Arithmetic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression. Nth Term of Progression is denoted by Tn symbol.

How to calculate Nth Term of Arithmetic Progression using this online calculator? To use this online calculator for Nth Term of Arithmetic Progression, enter First Term of Progression (a), Index N of Progression (n) & Common Difference of Progression (d) and hit the calculate button. Here is how the Nth Term of Arithmetic Progression calculation can be explained with given input values -> 23 = 3+(6-1)*4.

FAQ

What is Nth Term of Arithmetic Progression?
The Nth Term of Arithmetic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression and is represented as Tn = a+(n-1)*d or Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression. The First Term of Progression is the term at which the given Progression starts, The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression & The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.
How to calculate Nth Term of Arithmetic Progression?
The Nth Term of Arithmetic Progression formula is defined as the term corresponding to the index or position n from the beginning in the given Arithmetic Progression is calculated using Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression. To calculate Nth Term of Arithmetic Progression, you need First Term of Progression (a), Index N of Progression (n) & Common Difference of Progression (d). With our tool, you need to enter the respective value for First Term of Progression, Index N of Progression & Common Difference 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 First Term of Progression, Index N of Progression & Common Difference of Progression. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • 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 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 = ((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))
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