In the arithmetic sequence (or arithmetic progression) , ,,... 



each  is related to the previous  by a common difference, d.



This means we can write the progression as:



, , , ..., , ...



You are given  = -1  and  









Subtracting the  expression from the  expression:

   --> d = -3



With the common difference, you can easily find  and then write



  for n = 1,2,3,...



If you plug in n=22 you will find 





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EDITed to fix the display of the arithmetic progression (commas inside curly braces seem to break things).

 

Answer by ikleyn(52848)   (Show Source): You can put this solution on YOUR website!
 .





            There is a way to present the solution in a very short form.







Between the third term and the seventh term of an arithmetic progression, there are exactly 4 gaps in the number line 

of equal sizes.


Hence, the common difference of the arithmetic progression (which is exactly the size of a single gap) is

     =  = -3.


Thus we just found that the common difference of the AP is -3.


Now it is easy to find its first term   =  - 2*(-3) = -1 + 6 = 5.


Finally,   =  + d*(22-1) = 5 + (-3)*21 = -58.    ANSWER




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On arithmetic progressions, see the lessons



    - Arithmetic progressions



    - The proofs of the formulas for arithmetic progressions 



    - Problems on arithmetic progressions  



    - Word problems on arithmetic progressions



    - Chocolate bars and arithmetic progressions



    - One characteristic property of arithmetic progressions



    - Solved problems on arithmetic progressions 



    - Mathematical induction and arithmetic progressions



    - Mathematical induction for sequences other than arithmetic or geometric





Also,  you have this free of charge online textbook in ALGEBRA-II in this site



    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.





The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".







Save the link to this textbook together with its description





Free of charge online textbook in ALGEBRA-II

https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson





into your archive and use when it is needed.





 

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