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First Term of Arithmetic Progression given Pth and Qth Terms Formula

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GoFirst Term of Arithmetic Progression given Last Term Formula

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The First Term of Progression is the term at which the given Progression starts. Check FAQs

a = \frac{T p \cdot (q - 1) - T q \cdot (p - 1)}{q - p}

a - First 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?

First Term of Arithmetic Progression given Pth and Qth Terms Example

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

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

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

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

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

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

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First Term of Arithmetic Progression given Pth and Qth Terms Solution

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

FIRST Step Consider the formula

a = \frac{T p \cdot (q - 1) - T q \cdot (p - 1)}{q - p}

Next Step Substitute values of Variables

∴

a = \frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}

Next Step Prepare to Evaluate

∴

a = \frac{50 \cdot (8 - 1) - 80 \cdot (5 - 1)}{8 - 5}

LAST Step Evaluate

∴

a = 10

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

Variables

First Term of Progression

The First Term of Progression is the term at which the given Progression starts.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find First 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

Other Formulas to find First Term of Progression

Go First Term of Arithmetic Progression

a = T n - ((n - 1) \cdot d)

Go First Term of Arithmetic Progression given Last Term

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

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

First Term of Arithmetic Progression given Pth and Qth Terms evaluator uses First 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) to evaluate the First Term of Progression, The First Term of Arithmetic Progression given Pth and Qth Terms formula is defined as the term at which the given Arithmetic Progression starts, and calculated using the pth and qth terms of Arithmetic Progression. First Term of Progression is denoted by a symbol.

How to evaluate First Term of Arithmetic Progression given Pth and Qth Terms using this online evaluator? To use this online evaluator for First 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) and hit the calculate button.

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

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

The formula of First Term of Arithmetic Progression given Pth and Qth Terms is expressed as First 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). Here is an example- 94 = (50*(8-1)-80*(5-1))/(8-5).

How to calculate First 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) we can find First Term of Arithmetic Progression given Pth and Qth Terms using the formula - First 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).

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

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

First Term of Progression=Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)
First Term of Progression=Last Term of Progression-((Number of Total Terms of Progression-1)*Common Difference of Progression)

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First Term of Arithmetic Progression given Pth and Qth Terms Formula

​GoFirst Term of Arithmetic Progression Formula

​GoFirst Term of Arithmetic Progression given Last Term Formula

First Term of Arithmetic Progression given Pth and Qth Terms Example

First Term of Arithmetic Progression given Pth and Qth Terms Solution

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

Other Formulas to find First Term of Progression

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

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

Variable Name

GoFirst Term of Arithmetic Progression Formula

GoFirst Term of Arithmetic Progression given Last Term Formula