SOLUTION: the sum of the first and second terms of a geometric progression is 108 and the sum of the third and fourth is 12. find the two possible values of the common ratio and the correspo

Question 1171167: the sum of the first and second terms of a geometric progression is 108 and the sum of the third and fourth is 12. find the two possible values of the common ratio and the corresponding values of the first term

Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

then

..............eq.1

and the sum of the third and fourth is

since

we have

........substitute from eq.1

:
:
comes to factored numerator:

solutions:

or

since given , if

now find third and fourth term

then

and

now find third and fourth term

so, the two possible values of the common ratio and the corresponding values of the first term are:
1. and
2. and

Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!

The solution from the other tutor is a good example of the fact that there are practically endless ways to solve any given problem....

Here is a slightly simpler method.

(1) the sum of the 1st and 2nd terms is 108

(2) the sum of the 3rd and 4th terms is 12

Factor out a common factor on the left in (2); then substitute (1):

or

If r=1/3 then

ANSWER #1: a=81; r=1/3. The terms are 81, 27, 9, 3.

CHECK: 81+27 = 108; 9+3 = 12.

If r=-1/3 then

ANSWER #2: a=162; r=-1/3. The terms are 162, -54, 18, -6.

CHECK: 162+(-54) = 108; 18+(-6) = 12.

Answer by ikleyn(52879)   (Show Source): You can put this solution on YOUR website!
.

The post by @MathLover1 is a good example of EXTREMELY BAD approach and EXTREMELY BAD presentation.

It is an example of WHAT a SOLUTION SHOULD NOT be.

/\/\/\/\/\/\/\/

Dear @MathLover1

teaching Math and presenting solutions to Math problems should be easy and elegant - then (and only then)
the students will love Math.

Otherwise, they will HATE it . . .

If it is difficult for you to provide such teaching uniformly in many areas,
consider to focus in that areas where you are an expert.

Do not try to embrace everything - it is wrong way and wrong strategy . . .

Leave it to true experts . . .

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