SOLUTION: Find the first term of an Arithmetic sequence , whose 3rd term is 20 and its 6th term is

SOLUTION: Find the first term of an Arithmetic sequence , whose 3rd term is 20 and its 6th term is - 4 .

Question 1197283: Find the first term of an Arithmetic sequence , whose 3rd term is 20 and its 6th term is - 4 .
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
Find the first term of an Arithmetic sequence , whose 3rd term is 20 and its 6th term is - 4.
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Between the 3rd term and 6th term, there are 3 gaps of equal size on the number line.

The size of each gap is   =  = 8 units.


Hence, the common difference of this arithmetic sequence is d = -8 
    (it is exactly the gap size, but the sequence is decreasing, so the common difference is negative).


Next, the 1st term is 2 gaps backward from the 3rd term,
so, the 1st term is   = 20 - 2*(-8) = 20 + 16 = 36.


ANSWER.  First term of this arithmetic progression is 36.


CHECK.   =  = 36 + 5*(-8) = 36 - 40 = -4.   ! correct !

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
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".

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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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