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Topic: Hi. I'm a student from France. I have some mathematic questions that
i don't know to solve it

Replies: 6   Last Post: Sep 3, 2013 6:12 PM

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James Waldby

Posts: 348
Registered: 1/27/11
Re: Hi. I'm a student from France. I have some mathematic questions
that i don't know to solve it

Posted: Sep 3, 2013 3:26 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Tue, 03 Sep 2013 03:23:13 -0700, Taylor De Laurent wrote:

> Hi.My name is Taylor. I have some mathematic questions that i don't know to solve it. Is about a Arithematic and Geometric Progession questions
> Question: 1.The first term of a geometric progression exceeds 8 from the second term and the sum to infinity of the geometric progression is 18. Find the common ratio and the first term of the geometric progression.
> 2.The 8 term of an arithmetic progression is 20 and the 7 term is four times the 3 term.Find the first term and the common difference of the progression.


Writing a0, a1, etc for terms of series, in question 1 do you mean
that a0 = a1 + 8?

If so, write and solve the simultaneous equations s = 18 = a0 * 1/(1-r)
and a0 = a1 + 8 = a1 + r*a0. Eg, from the latter get a0 = 8/(1-r);
substitute that for a0 in the former; solve for r in the resulting
quadratic equation, and use the root with absolute value less than 1.

I haven't particularly looked at question 2, but you can write
several simultaneous equations a8 = 20 = a0 + 8*d where d is the common
difference; a7 = 4 * a3 = 4 * (a0 + 3*d); etc. [If by "The 8 term" you
mean the eighth term, write a7 in place of a8, or renumber starting with
a1 instead of a0, etc.]

--
jiw



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