SOLUTION: Find the first term & common difference if: 10th term is 35;15th terms is 55 2nd term is 56 ;12th term is 16 8th term is 4;18th term is -96 7th term is -25;2th term is -45

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Question 1087946: Find the first term & common difference if:
10th term is 35;15th terms is 55
2nd term is 56 ;12th term is 16
8th term is 4;18th term is -96
7th term is -25;2th term is -45

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
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Find the first term & common difference if:

1) 10th term is 35; 15th terms is 55
2) 2nd term is 56 ; 12th term is 16
3) 8th term is 4; 18th term is -96
4) 7th term is -25; 2th term is -45
~~~~~~~~~~~~~~~~~~~~~~

I will solve #1 only. Do the remaining cases following the same pattern.

1) 10th term is 35; 15th terms is 55.

   Between the 10-th and 15-th terms, there is the room for 5 (=15-10) common differences d.

   So,  5d = 55 - 35 = 20.  Hence, d =  = 4.

   Thus you just found the common difference d = 4.

   Then from  =  + 9*d  you have

              =  - 9d = 35 - 9*4 = 35 - 36 = -1.


Answer.   = -1;  d = 4.

Make the remaining cases following this pattern.


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".



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