IXL - Find the sum of an arithmetic series (Precalculus practice)

Find the sum of the finite arithmetic series.

(

–

)

ref_doc_title.

Learn with an example

question

Find the sum of the finite arithmetic series.

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–

)

key idea

A sequence is an ordered list of numbers. This list can have a finite number of terms or infinitely many terms.

A series is the sum of a sequence of numbers.

In sigma

notation,

the finite series

is written

where

is the

term in the sum and

is the

index.

The number 1 (from the equation

below the

)

is the lower limit of the series. The upper limit of the series is

A series is arithmetic if the differences between consecutive terms are all the same. There are two equivalent formulas for the sum of a finite arithmetic series:

Formula 1:

(

initial

final

)

Formula 2:

[

initial

(

–

)

]

where

is the number of terms,

initial

is the initial term in the series,

final

is the last term, and

is the difference between any two consecutive terms.

solution

Use either of the two formulas for the sum of a finite arithmetic series. For instance, here Formula 2 is used.

[

initial

(

–

)

]

First, find the number of terms,

The lower limit is 1 and the upper limit is 10. There are 10 integers from 1 to 10, inclusive, so

Next, find the initial term,

initial

Since the lower limit is 1, the initial term is

To find

plug

into the expression

–

initial

–

Finally, find the common difference,

by subtracting the

^th

term from the

(

)

^st

term. The

^th

term is

–

and the

(

)

^st

term is

(

)

–

[

(

)

^st

term

]

–

(

^th

term

)

–

(

–

)

Plug the values of

initial

and

into Formula 2 and simplify.

[

initial

(

–

)

]

[

(

–

)

]

235

The sum of the series is 235.

Looking for more? Try these:

Lesson: Arithmetic sequences

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Work it out

Not feeling ready yet? These can help:

BB.2Introduction to sigma notation

B.2Evaluate variable expressions involving integers

Lesson: Arithmetic sequences

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