Question 14977: complete the next two terms for the following sequence:-
5/7, 3/4, 7/9, 5/4, , ,
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The first step is to figure out the pattern. First look to see if there is a common number that you multiply the first number times to get the second, then the third, the fourth, etc. It doesn't look like there is a common factor that will do this, so it is not what we call a geometric sequence.
Second, see if there is a common number that can be added to get from the first number to the second, second to third, etc. Since there is no obvious common denominator, this does not appear to be the case.
So, see if there is a number that you can add to numerator and denominator that would make sense. Also, be aware that in the process of doing this, some of the fractions may have already been reduced to lowest terms. Try adding 1 to the numerator and denominator of 5/7. That would give you 6/8 which reduces to 3/4.
Continue by taking 6/8 and add 1 to the numerator and denominator. This gives 7/9 which is the third number.
Next, add 1 to numerator and denominator of 7/9 which would be 8/10 or 4/5. This is too close to what you have given as 5/4. I think maybe did you copy the problem wrong? If so, the PROBLEM should be
5/7, 3/4, 7/9, 4/5, , ,
The PATTERN would be the
5/7, 6/8, 7/9, 8/10, 9/11, and 9/12 or 3/4
And the SOLUTION would be the last two numbers in the sequence:
9/11 and 3/4.
If indeed you DID copy the problem correctly, then I am wrong. Please disregard this solution, and re-post the question, with my sincere apologies!!
R^2 at SCC
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