SOLUTION: Find a formula for an for the arithmetic sequence. a1 = −1, a5 = 23

Question 1178296: Find a formula for an for the arithmetic sequence.
a1 = −1, a5 = 23

Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
.


Between the first term  a1 = -1 and the fifth term a5 = 23, there is the distance of 24 units and 5-1 = 4 gaps 


of equal length.   Hence, each gap is   = 6 units long.


Thus the common difference of this arithmetic progression is  6 units.


Then the formula for the n-th term of the progression is


     =  + (n-1)*d = -1 + 6*(n-1) = 6n -7.


ANSWER.  The formula for the n-term is   = -1 + 6*(n-1)  or   = 6n -7

         You can chose any of these two versions: they are equivalent.

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Finding number of terms of an arithmetic progression
    - Inserting arithmetic means between given numbers
in this site.

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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