SOLUTION: the 10th term of an AP is -27 and the 5th term is -12. what is the 18th term. find also the sum of its 28th terms

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Question 1053935: the 10th term of an AP is -27 and the 5th term is -12. what is the 18th term. find also the sum of its 28th terms
Answer by ikleyn(52775) About Me  (Show Source):
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the 10th term of an AP is -27 and the 5th term is -12. what is the 18th term. find also the sum of its 28th terms
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(1)   a%5B10%5D = a%5B1%5D + 9*d,
(2)   a%5B5%5D  = a%5B1%5D + 4d.

or 

(1')  -27 = a%5B1%5D + 9*d,
(2')  -12  = a%5B1%5D + 4d.

Distract (2') from (1'). You will get

       -15 = 5d  --->  d = -3.

Then from (1') a%5B1%5D = -27 - 9*(-3) = -27 + 27 = 0.

Answer.  a%5B1%5D = 0,  d = -3.

         Now you can easily answer your questions.

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
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions

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".