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.]