Sum of Terms from Pth to Qth Terms of Arithmetic Progression Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression))
Sp-q = ((q-p+1)/2)*((2*a)+((p+q-2)*d))
This formula uses 5 Variables
Variables Used
Sum of Terms from Pth to Qth Terms of Progression - The Sum of Terms from Pth to Qth Terms of Progression is the summation of the terms starting from the pth term to the qth term of a 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.
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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
Common Difference of Progression - The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.
STEP 1: Convert Input(s) to Base Unit
Index Q of Progression: 8 --> No Conversion Required
Index P of Progression: 5 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Common Difference of Progression: 4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Sp-q = ((q-p+1)/2)*((2*a)+((p+q-2)*d)) --> ((8-5+1)/2)*((2*3)+((5+8-2)*4))
Evaluating ... ...
Sp-q = 100
STEP 3: Convert Result to Output's Unit
100 --> No Conversion Required
FINAL ANSWER
100 <-- Sum of Terms from Pth to Qth Terms of Progression
(Calculation completed in 00.004 seconds)

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8 Sum of Terms of Arithmetic Progression Calculators

Sum of Terms from Pth to Qth Terms of Arithmetic Progression
Go Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression))
Sum of Last N Terms of Arithmetic Progression
Go Sum of Last N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+(Common Difference of Progression*((2*Number of Total Terms of Progression)-Index N of Progression-1)))
Sum of Total Terms of Arithmetic Progression
Go Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*((2*First Term of Progression)+((Number of Total Terms of Progression-1)*Common Difference of Progression))
Sum of First N Terms of Arithmetic Progression
Go Sum of First N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+((Index N of Progression-1)*Common Difference of Progression))
Sum of Last N Terms of Arithmetic Progression given Last Term
Go Sum of Last N Terms of Progression = (Index N of Progression/2)*((2*Last Term of Progression)+(Common Difference of Progression*(1-Index N of Progression)))
Sum of Total Terms of Arithmetic Progression given Last Term
Go Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression)
Sum of Last N Terms of Arithmetic Progression given Nth Term from End
Go Sum of Last N Terms of Progression = (Index N of Progression/2)*(Last Term of Progression+Nth Term from End of Progression)
Sum of First N Terms of Arithmetic Progression given NthTerm
Go Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression)

11 Arithmetic Progression Calculators

Nth Term of Arithmetic Progression given Pth and Qth Terms
Go Nth 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))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))
Sum of Terms from Pth to Qth Terms of Arithmetic Progression
Go Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression))
Sum of Last N Terms of Arithmetic Progression
Go Sum of Last N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+(Common Difference of Progression*((2*Number of Total Terms of Progression)-Index N of Progression-1)))
Sum of First N Terms of Arithmetic Progression
Go Sum of First N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+((Index N of Progression-1)*Common Difference of Progression))
Nth Term from End of Arithmetic Progression
Go Nth Term from End of Progression = First Term of Progression+(Number of Total Terms of Progression-Index N of Progression)*Common Difference of Progression
Common Difference of Arithmetic Progression given Last Term
Go Common Difference of Progression = ((Last Term of Progression-First Term of Progression)/(Number of Total Terms of Progression-1))
Sum of Total Terms of Arithmetic Progression given Last Term
Go Sum of Total Terms of Progression = (Number of Total Terms of Progression/2)*(First Term of Progression+Last Term of Progression)
Number of Terms of Arithmetic Progression
Go Index N of Progression = ((Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1
First Term of Arithmetic Progression
Go First Term of Progression = Nth Term of Progression-((Index N of Progression-1)*Common Difference of Progression)
Nth Term of Arithmetic Progression
Go Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
Common Difference of Arithmetic Progression
Go Common Difference of Progression = Nth Term of Progression-(N-1)th Term of Progression

Sum of Terms from Pth to Qth Terms of Arithmetic Progression Formula

Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression))
Sp-q = ((q-p+1)/2)*((2*a)+((p+q-2)*d))

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 Sum of Terms from Pth to Qth Terms of Arithmetic Progression?

Sum of Terms from Pth to Qth Terms of Arithmetic Progression calculator uses Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression)) to calculate the Sum of Terms from Pth to Qth Terms of Progression, Sum of Terms from Pth to Qth Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the pth term to the qth term of given Arithmetic Progression. Sum of Terms from Pth to Qth Terms of Progression is denoted by Sp-q symbol.

How to calculate Sum of Terms from Pth to Qth Terms of Arithmetic Progression using this online calculator? To use this online calculator for Sum of Terms from Pth to Qth Terms of Arithmetic Progression, enter Index Q of Progression (q), Index P of Progression (p), First Term of Progression (a) & Common Difference of Progression (d) and hit the calculate button. Here is how the Sum of Terms from Pth to Qth Terms of Arithmetic Progression calculation can be explained with given input values -> 100 = ((8-5+1)/2)*((2*3)+((5+8-2)*4)).

FAQ

What is Sum of Terms from Pth to Qth Terms of Arithmetic Progression?
Sum of Terms from Pth to Qth Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the pth term to the qth term of given Arithmetic Progression and is represented as Sp-q = ((q-p+1)/2)*((2*a)+((p+q-2)*d)) or Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference 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, The Index P of Progression is the value of p for the pth term or the position of the pth term in the Progression, The First Term of Progression is the term at which the given Progression starts & The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.
How to calculate Sum of Terms from Pth to Qth Terms of Arithmetic Progression?
Sum of Terms from Pth to Qth Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the pth term to the qth term of given Arithmetic Progression is calculated using Sum of Terms from Pth to Qth Terms of Progression = ((Index Q of Progression-Index P of Progression+1)/2)*((2*First Term of Progression)+((Index P of Progression+Index Q of Progression-2)*Common Difference of Progression)). To calculate Sum of Terms from Pth to Qth Terms of Arithmetic Progression, you need Index Q of Progression (q), Index P of Progression (p), First Term of Progression (a) & Common Difference of Progression (d). With our tool, you need to enter the respective value for Index Q of Progression, Index P of Progression, First Term of Progression & Common Difference of Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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