SOLUTION: What is the twentieth term of the arithmetic sequence 21, 18, 15, 12

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Question 1169306: What is the twentieth term of the arithmetic sequence 21, 18, 15, 12
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
.

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
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.



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the arithmetic sequence formula :
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d where a%5Bn%5D is n-th term, a%5B1%5D is 1-th term , n is total number of terms, and d is difference between two consecutive terms
in yuor case
a%5B1%5D=21
d=-3
you need the twentieth term, so n=20
so, you have:
a%5B20%5D=21%2B%2820-1%29%28-3%29
a%5B20%5D=21-%2819%29%283%29
a%5B20%5D=21-57
a%5B20%5D=-36
the twentieth term of the arithmetic sequence 21, 18, 15, 12 is -36