First Term of Arithmetic Progression given Pth and Qth Terms Calculator

✖The Pth Term of Progression is the term corresponding to the index or position p from the beginning of the given Progression.ⓘ Pth Term of Progression [T_p]			+10% -10%
✖The Index Q of Progression is the value of q for the qth term or the position of the qth term in the Progression.ⓘ Index Q of Progression [q]			+10% -10%
✖The Qth Term of Progression is the term corresponding to the index or position q from the beginning of the given Progression.ⓘ Qth Term of Progression [T_q]			+10% -10%
✖The Index P of Progression is the value of p for the pth term or the position of the pth term in the Progression.ⓘ Index P of Progression [p]			+10% -10%

✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Arithmetic Progression given Pth and Qth Terms [a]

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First Term of Arithmetic Progression given Pth and Qth Terms Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
a = (T_p*(q-1)-T_q*(p-1))/(q-p)
This formula uses 5 Variables

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Pth Term of Progression: 50 --> No Conversion Required
Index Q of Progression: 8 --> No Conversion Required
Qth Term of Progression: 80 --> No Conversion Required
Index P of Progression: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = (T_p*(q-1)-T_q*(p-1))/(q-p) --> (50*(8-1)-80*(5-1))/(8-5)

Evaluating ... ...

a = 10

STEP 3: Convert Result to Output's Unit

10 --> No Conversion Required

FINAL ANSWER

10 <-- First Term of Progression

(Calculation completed in 00.020 seconds)

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< First Term of Arithmetic Progression Calculators

First Term of Arithmetic Progression given Pth and Qth Terms

LaTeX Go 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)

First Term of Arithmetic Progression given Last Term

LaTeX Go First Term of Progression = Last Term of Progression-((Number of Total Terms of Progression-1)*Common Difference of Progression)

First Term of Arithmetic Progression

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

First Term of Arithmetic Progression given Pth and Qth Terms Formula

LaTeX Go

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 First Term of Arithmetic Progression given Pth and Qth Terms?

First Term of Arithmetic Progression given Pth and Qth Terms calculator 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 calculate 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 calculate First Term of Arithmetic Progression given Pth and Qth Terms using this online calculator? To use this online calculator 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. Here is how the First Term of Arithmetic Progression given Pth and Qth Terms calculation can be explained with given input values -> 94 = (50*(8-1)-80*(5-1))/(8-5).

FAQ

What is First Term of Arithmetic Progression given Pth and Qth Terms?

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 and is represented as a = (T_p*(q-1)-T_q*(p-1))/(q-p) or 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). The Pth Term of Progression is the term corresponding to the index or position p from the beginning of the given 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, The Qth Term of Progression is the term corresponding to the index or position q from the beginning of the given 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.

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

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 is calculated using 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 calculate First Term of Arithmetic Progression given Pth and Qth Terms, you need Pth Term of Progression (T_p), Index Q of Progression (q), Qth Term of Progression (T_q) & Index P of Progression (p). With our tool, you need to enter the respective value for Pth Term of Progression, Index Q of Progression, Qth Term of Progression & Index P 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 First Term of Progression?

In this formula, First Term of Progression uses Pth Term of Progression, Index Q of Progression, Qth Term of Progression & Index P of Progression. We can use 2 other way(s) to calculate the same, which is/are as follows -

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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