SOLUTION: Find the first term and the common difference of the arithmetic sequence whose 7th term is -30 and 12th term is -55. first term common difference

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Question 1126169: Find the first term and the common difference of the arithmetic sequence whose
7th term is -30 and 12th term is -55.
first term
common difference

Answer by ikleyn(52793) About Me  (Show Source):
You can put this solution on YOUR website!
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There are 5 gaps between the 7th term and 12th term.


Therefore, the common difference is   d = %28%28-55%29-%28-30%29%29%2F5 = -5.


Then  from  a%5B7%5D = a%5B1%5D + 6*d you have


    a%5B1%5D = a%5B7%5D - 6*d = -30 - 6*(-5) = -30 + 30 = 0.

I answered all the questions.

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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".


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.