intend a sequence of number is arithmetic (that is, it increases or to reduce by a consistent amount each term), and also you desire to find the sum of the first n terms.

denote this partial amount by S n . Then

S n = n ( a 1   +   a n ) 2 , where n is the number of terms, a 1 is the an initial term and a n is the critical term.

The amount of the an initial n terms of an arithmetic succession is referred to as an arithmetic series .

example 1:

find the sum of the an initial 20 regards to the arithmetic series if a 1 = 5 and a 20 = 62 .

S 20 = 20 ( 5   +   62 ) 2 S 20 = 670

instance 2:

find the sum of the an initial 40 terms of the arithmetic succession 2 , 5 , 8 , 11 , ⋯ .

first find the 40 th term:

a 40 = a 1 + ( n − 1 ) d                 = 2 + 39 ( 3 ) = 119

Then uncover the sum:

S n = n ( a 1   +   a n ) 2 S 40 = 40 ( 2   +   119 ) 2 = 2420

example 3:

discover the sum:

∑ k = 1 50 ( 3 k + 2 )

first find a 1 and also a 50 :

a 1 = 3 ( 1 ) + 2 = 5 a 50 = 3 ( 50 ) + 2 = 152

Then uncover the sum:

S k = k ( a 1   +   a k ) 2 S 50 = 50 ( 5   +   152 ) 2 = 3925

view also: sigma notation the a series and nth term of one arithmetic succession

Subjects close to Me
Mandarin Chinese Tutors sat Test prep ISEE-Middle Level Verbal reasoning Tutors Statway Tutors Nematology Tutors SAT topic Tests test Prep GRE test Prep C2 courses & classes Subcellular company Tutors PARCC test Prep HSPT test Prep middle School mathematics Tutors COMLEX process & classes ACSM - American college of Sports medicine Test Prep speak to Of Duty: black color Ops III Tutors SAT topic Test in biologic E/M process & class Computational Statistics Tutors CSRM - Certified institution Risk Manager courses & classes Ladin Tutors CLEP values of Macroeconomics Tutors
Popular Cities
Orlando Tutoring Atlanta Tutoring Albuquerque Tutoring Tulsa Tutoring Syracuse Tutoring Houston Tutoring Miami Tutoring Ann Arbor Tutoring Albany Tutoring Austin Tutoring
Popular Subjects
act Tutors in Philadelphia Physics Tutors in Chicago analysis Tutors in Phoenix English Tutors in Philadelphia Statistics Tutors in Boston ISEE Tutors in Seattle sat Tutors in Los Angeles GMAT Tutors in san Diego Spanish Tutors in Denver Algebra Tutors in mountain Francisco-Bay Area

### Download our cost-free learning tools apps and also test prepare books

Varsity Tutors
Our Company
Free Resources
Top Subjects
Top Locations

Names of standardization tests room owned by the trademark holders and also are not affiliated through Varsity Tutors LLC.

You are watching: The sequence whose nth term is the sum of the first n positive integers

*See complete details for much better Score Guarantee.

Media outlet trademarks are owned by the particular media outlets and are not affiliated through Varsity Tutors.

Award-Winning claim based upon CBS Local and also Houston push awards.

Varsity Tutors does not have affiliation with universities discussed on its website.

See more: Which Fast-Food Chain Offers Tableside Service On Valentine’S Day

Varsity Tutors associate learners with experts. Instructors are independent contractors who continue their solutions to every client, using their very own style,methods and also materials.