Sum of First N Terms of Arithmetic Progression given NthTerm Calculator

✖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 First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%
✖The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.ⓘ Nth Term of Progression [T_n]			+10% -10%

✖The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression.ⓘ Sum of First N Terms of Arithmetic Progression given NthTerm [S_n]

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Sum of First N Terms of Arithmetic Progression given NthTerm

Formula

`"S"_{"n"} = ("n"/2)*("a"+"T"_{"n"})`

Example

`"189"=("6"/2)*("3"+"60")`

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Sum of First N Terms of Arithmetic Progression given NthTerm Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression)
S_n = (n/2)*(a+T_n)
This formula uses 4 Variables

Variables Used

Sum of First N Terms of Progression - The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given 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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
Nth Term of Progression - The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.

STEP 1: Convert Input(s) to Base Unit

Index N of Progression: 6 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Nth Term of Progression: 60 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_n = (n/2)*(a+T_n) --> (6/2)*(3+60)

Evaluating ... ...

S_n = 189

STEP 3: Convert Result to Output's Unit

189 --> No Conversion Required

FINAL ANSWER

189 <-- Sum of First N 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)

Sum of First N Terms of Arithmetic Progression given NthTerm Formula

Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression)
S_n = (n/2)*(a+T_n)

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 First N Terms of Arithmetic Progression given NthTerm?

Sum of First N Terms of Arithmetic Progression given NthTerm calculator uses Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression) to calculate the Sum of First N Terms of Progression, The Sum of First N Terms of Arithmetic Progression given NthTerm formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Progression, and is calculated using the nth term of the given Arithmetic Progression. Sum of First N Terms of Progression is denoted by S_n symbol.

How to calculate Sum of First N Terms of Arithmetic Progression given NthTerm using this online calculator? To use this online calculator for Sum of First N Terms of Arithmetic Progression given NthTerm, enter Index N of Progression (n), First Term of Progression (a) & Nth Term of Progression (T_n) and hit the calculate button. Here is how the Sum of First N Terms of Arithmetic Progression given NthTerm calculation can be explained with given input values -> 189 = (6/2)*(3+60).

FAQ

What is Sum of First N Terms of Arithmetic Progression given NthTerm?

The Sum of First N Terms of Arithmetic Progression given NthTerm formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Progression, and is calculated using the nth term of the given Arithmetic Progression and is represented as S_n = (n/2)*(a+T_n) or Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term 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, The First Term of Progression is the term at which the given Progression starts & The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.

How to calculate Sum of First N Terms of Arithmetic Progression given NthTerm?

The Sum of First N Terms of Arithmetic Progression given NthTerm formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Progression, and is calculated using the nth term of the given Arithmetic Progression is calculated using Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression). To calculate Sum of First N Terms of Arithmetic Progression given NthTerm, you need Index N of Progression (n), First Term of Progression (a) & Nth Term of Progression (T_n). With our tool, you need to enter the respective value for Index N of Progression, First Term of Progression & Nth Term 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 Sum of First N Terms of Progression?

In this formula, Sum of First N Terms of Progression uses Index N of Progression, First Term of Progression & Nth Term of Progression. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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