SOLUTION: Pls help me solve this: 1):the 2pth term of an A.P is 50 more than the pth term and the (p+1)th term is 56.find the first term.. 2): A G.P is such that the 3rd term minus the fir

Question 1139290: Pls help me solve this: 1):the 2pth term of an A.P is 50 more than the pth term and the (p+1)th term is 56.find the first term..
2): A G.P is such that the 3rd term minus the first term is 48.the 4th minus the second term is 44.find the common ratio, the first term and the 12th term.
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

I will solve part 1) only in my post.

Between  (2p)-th and p-th terms, there are exactly  "p" gaps (each gap size is exactly the common difference).


So, "p" gaps make 50, in total.


Also, there are 50 gaps between (p+1)-the term and 1-st term.


In other words, the difference between    and    is  50.


We are also given that   = 56.


Hence,   = 56 - 50 = 6.     ANSWER

Solved.

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On arithmetic progressions, see introductory lessons
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    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

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The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

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Now I'll explain you, why I solved only # 1) problem of your post.

It because there is a   R U L E   in this forum:

One and only one problem per post.

If you want to get all benefits from visiting this forum, then P L E A S E follow this rule.

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