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Last Term of Arithmetic Progression given Pth and Qth Terms Formula

GoLast Term of Arithmetic Progression Formula

GoLast Term of Arithmetic Progression given Sum of Last N Terms Formula

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The Last Term of Progression is the term at which the given Progression terminates. Check FAQs

l = (\frac{T p \cdot (q - 1) - T q \cdot (p - 1)}{q - p}) + (n Total - 1) \cdot (\frac{T q - T p}{q - p})

l - Last Term of Progression?T_p - Pth Term of Progression?q - Index Q of Progression?T_q - Qth Term of Progression?p - Index P of Progression?n_Total - Number of Total Terms of Progression?

Last Term of Arithmetic Progression given Pth and Qth Terms Example

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Here is how the Last Term of Arithmetic Progression given Pth and Qth Terms equation looks like with Values.

Here is how the Last Term of Arithmetic Progression given Pth and Qth Terms equation looks like with Units.

Here is how the Last Term of Arithmetic Progression given Pth and Qth Terms equation looks like.

100 = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (10 - 1) \cdot (\frac{80 - 50}{8 - 5})

100 = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (10 - 1) \cdot (\frac{80 - 50}{8 - 5})

100 = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (10 - 1) \cdot (\frac{80 - 50}{8 - 5})

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Last Term of Arithmetic Progression given Pth and Qth Terms Solution

Follow our step by step solution on how to calculate Last Term of Arithmetic Progression given Pth and Qth Terms?

FIRST Step Consider the formula

l = (\frac{T p \cdot (q - 1) - T q \cdot (p - 1)}{q - p}) + (n Total - 1) \cdot (\frac{T q - T p}{q - p})

Next Step Substitute values of Variables

∴

l = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (10 - 1) \cdot (\frac{80 - 50}{8 - 5})

Next Step Prepare to Evaluate

∴

l = (\frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}) + (10 - 1) \cdot (\frac{80 - 50}{8 - 5})

LAST Step Evaluate

∴

l = 100

Last Term of Arithmetic Progression given Pth and Qth Terms Formula Elements

Variables

Last Term of Progression

The Last Term of Progression is the term at which the given Progression terminates.

Symbol: l

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Last Term of 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.

Symbol: T_p

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Pth Term of 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.

Symbol: q

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Index Q of 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.

Symbol: T_q

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Qth Term of 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.

Symbol: p

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Index P of 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.

Symbol: n_Total

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Total Terms of Progression

Other Formulas to find Last Term of Progression

Go Last Term of Arithmetic Progression

l = a + ((n Total - 1) \cdot d)

Go Last Term of Arithmetic Progression given Sum of Last N Terms

l = (\frac{S n(End)}{n} - \frac{d \cdot (1 - n)}{2})

Go Last Term of Arithmetic Progression given Sum of Total Terms

l = (\frac{2 \cdot S Total}{n Total}) - a

Go Last Term of Arithmetic Progression given Nth Term

l = a + (n Total - 1) \cdot (\frac{T n - a}{n - 1})

How to Evaluate Last Term of Arithmetic Progression given Pth and Qth Terms?

Last Term of Arithmetic Progression given Pth and Qth Terms evaluator uses Last 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))+(Number of Total Terms of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)) to evaluate the Last Term of Progression, The Last Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term at which the given Arithmetic Progression terminates and calculated using the pth and qth terms of the Arithmetic Progression. Last Term of Progression is denoted by l symbol.

How to evaluate Last Term of Arithmetic Progression given Pth and Qth Terms using this online evaluator? To use this online evaluator for Last 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) & Number of Total Terms of Progression (n_Total) and hit the calculate button.

FAQs on Last Term of Arithmetic Progression given Pth and Qth Terms

What is the formula to find Last Term of Arithmetic Progression given Pth and Qth Terms?

The formula of Last Term of Arithmetic Progression given Pth and Qth Terms is expressed as Last 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))+(Number of Total Terms of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)). Here is an example- -5 = ((50*(8-1)-80*(5-1))/(8-5))+(10-1)*((80-50)/(8-5)).

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

With Pth Term of Progression (T_p), Index Q of Progression (q), Qth Term of Progression (T_q), Index P of Progression (p) & Number of Total Terms of Progression (n_Total) we can find Last Term of Arithmetic Progression given Pth and Qth Terms using the formula - Last 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))+(Number of Total Terms of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression)).

What are the other ways to Calculate Last Term of Progression?

Here are the different ways to Calculate Last Term of Progression-

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

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Last Term of Arithmetic Progression given Pth and Qth Terms Formula

​GoLast Term of Arithmetic Progression Formula

​GoLast Term of Arithmetic Progression given Sum of Last N Terms Formula

Last Term of Arithmetic Progression given Pth and Qth Terms Example

Last Term of Arithmetic Progression given Pth and Qth Terms Solution

Last Term of Arithmetic Progression given Pth and Qth Terms Formula Elements

Other Formulas to find Last Term of Progression

How to Evaluate Last Term of Arithmetic Progression given Pth and Qth Terms?

FAQs on Last Term of Arithmetic Progression given Pth and Qth Terms

Variable Name

GoLast Term of Arithmetic Progression Formula

GoLast Term of Arithmetic Progression given Sum of Last N Terms Formula