Nth Term from End of Geometric Progression given Last Term Calculator

✖The Last Term of Progression is the term at which the given Progression terminates.ⓘ Last Term of Progression [l]			+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 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 given Last Term [T_n(End)]

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Nth Term from End of Geometric Progression given Last Term Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Term from End of Progression = Last Term of Progression/(Common Ratio of Progression^(Index N of Progression-1))
T_n(End) = l/(r^(n-1))
This formula uses 4 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.
Last Term of Progression - The Last Term of Progression is the term at which the given Progression terminates.
Common Ratio of Progression - The Common Ratio of Progression is the ratio of any term to its preceding term of 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

Last Term of Progression: 100 --> No Conversion Required
Common Ratio of Progression: 2 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n(End) = l/(r^(n-1)) --> 100/(2^(6-1))

Evaluating ... ...

T_n(End) = 3.125

STEP 3: Convert Result to Output's Unit

3.125 --> No Conversion Required

FINAL ANSWER

3.125 <-- Nth Term from End of Progression

(Calculation completed in 00.008 seconds)

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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

Nth Term from End of Geometric Progression given Last Term Formula

LaTeX Go

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

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 given Last Term?

Nth Term from End of Geometric Progression given Last Term calculator uses Nth Term from End of Progression = Last Term of Progression/(Common Ratio of Progression^(Index N of Progression-1)) to calculate the Nth Term from End of Progression, The Nth Term from End of Geometric Progression given Last Term formula is defined as the term corresponding to the index or position n starting from the end of the given Geometric Progression, calculated using the last term. Nth Term from End of Progression is denoted by T_n(End) symbol.

How to calculate Nth Term from End of Geometric Progression given Last Term using this online calculator? To use this online calculator for Nth Term from End of Geometric Progression given Last Term, enter Last Term of Progression (l), Common Ratio of Progression (r) & Index N of Progression (n) and hit the calculate button. Here is how the Nth Term from End of Geometric Progression given Last Term calculation can be explained with given input values -> 3.125 = 100/(2^(6-1)).

FAQ

What is Nth Term from End of Geometric Progression given Last Term?

The Nth Term from End of Geometric Progression given Last Term formula is defined as the term corresponding to the index or position n starting from the end of the given Geometric Progression, calculated using the last term and is represented as T_n(End) = l/(r^(n-1)) or Nth Term from End of Progression = Last Term of Progression/(Common Ratio of Progression^(Index N of Progression-1)). The Last Term of Progression is the term at which the given Progression terminates, The Common Ratio of Progression is the ratio of any term to its preceding term of 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 from End of Geometric Progression given Last Term?

The Nth Term from End of Geometric Progression given Last Term formula is defined as the term corresponding to the index or position n starting from the end of the given Geometric Progression, calculated using the last term is calculated using Nth Term from End of Progression = Last Term of Progression/(Common Ratio of Progression^(Index N of Progression-1)). To calculate Nth Term from End of Geometric Progression given Last Term, you need Last Term of Progression (l), Common Ratio of Progression (r) & Index N of Progression (n). With our tool, you need to enter the respective value for Last Term of Progression, Common Ratio 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 Last Term of Progression, Common Ratio 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 = First Term of Progression*(Common Ratio of Progression^(Number of Total Terms of Progression-Index N of Progression))

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