Question 1197285: Find the sum to Infinity of the following Sequence : 18, 12, 8, . . .
Found 3 solutions by greenestamps, math_tutor2020, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Note that, technically, the question can't be answered, because there are an infinite number of sequences whose first three terms are 18, 12, and 8. The correct statement of the problem is
Find the sum to infinity of the following GEOMETRIC sequence : 18, 12, 8, . . .
What do you need help with on this problem? There is a simple formula for the sum of an infinite geometric sequence:
(first term) divided by (1 minus the common ratio)
You are given the first term; to find the common ratio, divide the 2nd term by the 1st (or the 3rd term by the 2nd).
Then do the simple arithmetic.
If you are having trouble doing that, then re-post the question, telling (as you are instructed to do when making posts to this forum) exactly what it is about the problem that you need help with.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
a = 18 = first term
Assuming this sequence is geometric, then,
r = common ratio
r = (term2)/(term1)
r = 12/18
r = 2/3
Or
r = (term3)/(term2)
r = 8/12
r = 2/3
2/3 = 0.667 approximately
Since -1 < r < 1 is true, this means the infinitely many terms of this sequence add to some fixed value S
S = a/(1-r)
S = 18/(1-2/3)
S = 18/(3/3-2/3)
S = 18/(1/3)
S = 18*3/1
S = 54
Answer: 54
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
In this my post I want to explain you WHY your problem formulation is INCORRECT.
When you say " Find the sum to Infinity of the following Sequence : 18, 12, 8, . . .",
the sequence is, actually, UNDEFINED : we don't know how to continue it.
We only can hypothesize, what the sequence, actually, is, but making such hypotheses is not the way to solve Math problems.
In Math textbooks, such formulations are NEVER USED and are not allowable:
NO ONE professional Math writer will write this way.
The correct formulation is " Find the sum to infinity of the following geometric sequence: 18, 12, 8, . . .".
Then the sequence is defined by a UNIQUE way, and the problem is good for the solution.
As a joke, I say it every day, that Math composers of this forum got their mathematical education from reading puzzles.
Which means very low level of mathematical education, not sufficient for writing Math problems.
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