Nth Term from End of Geometric Progression Calculator

✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%
✖The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.ⓘ Common Ratio of Progression [r]			+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 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 from End of Progression is the term corresponding to the index or position n from the end of the given Progression.ⓘ Nth Term from End of Geometric Progression [T_n(End)]

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Nth Term from End of Geometric Progression Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Term from End of Progression = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression))
T_n(End) = a*(r^(n_Total-n))
This formula uses 5 Variables

Variables Used

Nth Term from End of Progression - The Nth Term from End of Progression is the term corresponding to the index or position n from the end of the given Progression.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
Common Ratio of Progression - The Common Ratio of Progression is the ratio of any term to its preceding term of 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.
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

First Term of Progression: 3 --> No Conversion Required
Common Ratio of Progression: 2 --> No Conversion Required
Number of Total Terms of Progression: 10 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n(End) = a*(r^(n_Total-n)) --> 3*(2^(10-6))

Evaluating ... ...

T_n(End) = 48

STEP 3: Convert Result to Output's Unit

48 --> No Conversion Required

FINAL ANSWER

48 <-- Nth Term from End of Progression

(Calculation completed in 00.008 seconds)

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< Nth Term of Geometric Progression Calculators

Nth Term from End of Geometric Progression

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

Nth Term from End of Geometric Progression given Last Term

LaTeX Go Nth Term from End of Progression = Last Term of Progression/(Common Ratio of Progression^(Index N of Progression-1))

Nth Term of Geometric Progression

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

Nth Term of Geometric Progression given (N-1)th Term

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

< Geometric Progression Calculators

Sum of First N Terms of Geometric Progression

LaTeX Go Sum of First N Terms of Progression = (First Term of Progression*(Common Ratio of Progression^Index N of Progression-1))/(Common Ratio of Progression-1)

Nth Term of Geometric Progression

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

Sum of Infinite Geometric Progression

LaTeX Go Sum of Infinite Progression = First Term of Progression/(1-Common Ratio of Infinite Progression)

Common Ratio of Geometric Progression

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

Nth Term from End of Geometric Progression Formula

LaTeX Go

Nth Term from End of Progression = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression))
T_n(End) = a*(r^(n_Total-n))

What is a Geometric Progression?

In Mathematics a Geometric Progression or simply GP also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed real number called the common ratio. For example, the sequence 2, 6, 18, 54,... is a Geometric Progression with common ratio 3. If the sum of all terms in the progression is a finite number or if the infinite sum of the progression exists then the we say it is an Infinite Geometric Progression or Infinite GP. And if the infinite sum of the progression does not exist, then it is a Finite Geometric Progression or Finite GP. If the absolute value of the common ratio is greater than 1 then the GP will be a Finite GP and if it is less than 1 then the GP will be an Infinite GP.

How to Calculate Nth Term from End of Geometric Progression?

Nth Term from End of Geometric Progression calculator uses Nth Term from End of Progression = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression)) to calculate the Nth Term from End of Progression, The Nth Term from End of Geometric Progression formula is defined as the term corresponding to the index or position n starting from the end of the given Geometric Progression. Nth Term from End of Progression is denoted by T_n(End) symbol.

How to calculate Nth Term from End of Geometric Progression using this online calculator? To use this online calculator for Nth Term from End of Geometric Progression, enter First Term of Progression (a), Common Ratio of Progression (r), Number of Total Terms of Progression (n_Total) & Index N of Progression (n) and hit the calculate button. Here is how the Nth Term from End of Geometric Progression calculation can be explained with given input values -> 12 = 3*(2^(10-6)).

FAQ

What is Nth Term from End of Geometric Progression?

The Nth Term from End of Geometric Progression formula is defined as the term corresponding to the index or position n starting from the end of the given Geometric Progression and is represented as T_n(End) = a*(r^(n_Total-n)) or Nth Term from End of Progression = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression)). The First Term of Progression is the term at which the given Progression starts, The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression, The Number of Total Terms of Progression is the total number of terms present in the given sequence 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.

How to calculate Nth Term from End of Geometric Progression?

The Nth Term from End of Geometric Progression formula is defined as the term corresponding to the index or position n starting from the end of the given Geometric Progression is calculated using Nth Term from End of Progression = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression)). To calculate Nth Term from End of Geometric Progression, you need First Term of Progression (a), Common Ratio of Progression (r), Number of Total Terms of Progression (n_Total) & Index N of Progression (n). With our tool, you need to enter the respective value for First Term of Progression, Common Ratio of Progression, Number of Total Terms 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 from End of Progression?

In this formula, Nth Term from End of Progression uses First Term of Progression, Common Ratio of Progression, Number of Total Terms of Progression & Index N of Progression. We can use 1 other way(s) to calculate the same, which is/are as follows -

Nth Term from End of Progression = Last Term of Progression/(Common Ratio of Progression^(Index N of Progression-1))

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