Question 714016: The fourth, seventh and sixteenth terms of arithmetic series form a geometric series. If the first six terms of arithmetic series have a sum of 12.
(a) Find the common difference of the arithmetic series
(b) Calculate the common ratio of the geometric series
Answer by kevwill(135)   (Show Source):
You can put this solution on YOUR website! If x is the value of the first term, and d is the difference between terms, then the first 6 terms of the arithmetic series are:
 ,  ,  ,  ,  , 
The sum of these 6 terms is 12, so we have:
The 4rd, 7th, and 16th terms, a geometric series, are
,  , and 
So we know that
Multiplying both sides by 
 where  (If  we have the trivial sequence  , , , , , ...)
Plugging  into
And plugging into
So our series is:
 ,  ,  ,  ,  ,  , ...
The 4th, 7th, and 16th terms are ,  , and 
So the difference in the arithmetic sequence is 2 and the ratio in the geometric sequence is 3.
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