SOLUTION: the third term of an A.P is 16 and its 6th term is 34 .find a:the common difference b:the first

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Question 1084122: the third term of an A.P is 16 and its 6th term is 34 .find a:the common difference b:the first term c:the 20th term d:the sum of the first and 20 terms
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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a%5B3%5D = a%5B1%5D%2B2d = 16,   (1)

a%5B6%5D = a%5B1%5D%2B5d = 34.   (2)


====>  3d = 34 - 16 = 18  ====>  d = 18%2F3 = 6.


Then a%5B1%5D = a%5B3%5D+-+2%2Ad = 16 - 2*6 = 4.


Then a%5B20%5D = a%5B1%5D+%2B+19%2Ad = 4 + 19*6 = 118.


Then the sum of the first 20 terms is

S%5B20%5D = %28a%5B1%5D%2Ba%5B20%5D%29%2F2.20 = %284+%2B+118%29%2F2.20 = 1220.

Solved.


There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on 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".