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Arithmetic Sequences and Series Worksheet, Lecture notes of Calculus

Centro Escolar University (CEU)Calculus

This worksheet covers determining arithmetic sequences, finding common differences, explicit and recursive formulas, and evaluating arithmetic series. It includes practice problems and solutions.

Typology: Lecture notes

2021/2022

Uploaded on 08/05/2022

hal_s95
hal_s95 🇵🇭

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©S R2a0e1c6X zKIuutYaE ]SooAfutnwmaCrheZ sLlLbCX.` R VAalPlQ ^rpipghhAtTsO IrNeUsheJrkvkezdR.Y i cMzaFdSeo ]wZigtyhW qIbnZfniunmiXtZeO NPvrPeKcqa_lHcyuzlpuwsV.
Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Arithmetic Sequences and Series
Name___________________________________
Date________________ Period____
-1-
Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the
explicit formula, and the three terms in the sequence after the last one given.
1) , , , , ... 2) , , , , ...
3) ,
, ,
, ... 4) , , , , ...
Given the explicit formula for an arithmetic sequence find the common difference, the term
named in the problem, and the recursive formula.
5) ann
Find a
6) an

n
Find a
Given two terms in an arithmetic sequence find the common difference, the explicit formula, and
the recursive formula.
7) a
 and a
 8) a
 and a

Find the missing terms in each arithmetic sequence.
9) ...,
, ___, ___, , ... 10) ..., , ___, ___, , ...
pf3
pf4

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©S R2a0e1c6X zKIuutYaE ]SooAfutnwmaCrheZ sLlLbCX.` R VAalPlQ ^rpipghhAtTsO IrNeUsheJrkvkezdR.Y i cMzaFdSeo ]wZigtyhW qIbnZfniunmiXtZeO NPvrPeKcqa_lHcyuzlpuwsV. Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus

Arithmetic Sequences and Series

Name___________________________________ Date________________ Period____ -1- Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the explicit formula, and the three terms in the sequence after the last one given.

  1. , , , , ... 2) , , , , ...

3) , 

 , ,   , ... 4)^ ,^ ,^ ,^ , ...

Given the explicit formula for an arithmetic sequence find the common difference, the term named in the problem, and the recursive formula.

  1. an  n Find a 
  2. an   

n Find a  Given two terms in an arithmetic sequence find the common difference, the explicit formula, and the recursive formula.

  1. a  and a  8) a  and a  Find the missing terms in each arithmetic sequence.
  2. ...,  

, ___, ___, , ... 10) ...,^ , ___, ___,^ , ...

©u S2[0z1t6O cKNuQtZaa ^S[ojfrtHw]aerWey NLGLXCM.g X rAclFls TrpiggfhotWsQ Kr_eqsme[rYvsepda.O N NMKa^ddeb Iwpiltsh] AIwnWf^i^nmiBtXed uPArSeUcIaclvcjuGlcuQsT. -2- Worksheet by Kuta Software LLC Evaluate the related series of each sequence.

  1. , , ,  12) , , , , , ,  Evaluate each arithmetic series described.
  2. a   , d   , n  14)^ a ,^ d ,^ n 
  3. a , a (^) n , n  16) a , an , n 

m  

m ) 18) 

n  

( n )

m  

( m ) 20) 

k  

k )

i  

( i ) 22) 

n  

( n )

Determine the number of terms n in each arithmetic series.

23) ()()()^ ..., S n  24) ..., S n 

©Y h2n0j1i6l TKkuTtIaZ XS\o_fjtMwiaxrkeA ]LfLYCq.v T WAqlml^ xrjicgohBtwsB BrdeYsDeOr\vbegd^.T t jMwa\daea twciXtwhh WIqnAfri^nmiotGeF SPwrRercaaGlKcluclOuls[. -2- Worksheet by Kuta Software LLC Evaluate the related series of each sequence.

  1. , , ,  

Evaluate each arithmetic series described.

  1. a   , d   , n   
  2. a , d , n  
  3. a , a (^) n , n  
  4. a , an , n  

m  

m )

n  

( n )

m  

( m )

k  

k )

i  

( i )

n  

( n )

Determine the number of terms n in each arithmetic series.

23) ()()()^ ..., S n 

  1. ..., S (^) n   Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com