For the following arithmetic sequence: determine the common difference. Find the next three terms of the sequence.

e) 2/3 , 1/15, -8/15

I really don't get how to solve this one, I see no pattern :\

I do believe that all the denominators need to be the same to see the pattern. 2/3 is the same as 10/15 so the pattern looks like 10/15, 1/15, -8/15. Subtracting 9 from the top set of #'s

Oh I get it now. Thanks soo much Jess :)

To determine the common difference of an arithmetic sequence, you need to find the difference between any two consecutive terms in the sequence. Once you find the common difference, you can use it to find the next terms of the sequence.

In your example, let's find the common difference between the first two terms:

Common difference = (second term) - (first term)
= (1/15) - (2/3)

To subtract fractions, you need to have a common denominator. In this case, the common denominator is 15.

Common difference = (1/15) - (10/15)
= -9/15

Simplified, the common difference is -3/5.

Now that we have the common difference, we can find the next three terms of the sequence by repeatedly adding the common difference to the previous term.

To find the third term:
third term = (second term) + (common difference)
= (1/15) + (-3/5)

To add fractions, you need to have a common denominator. In this case, the common denominator is 15.

third term = (1/15) + (-9/15)
= -8/15

Now, to find the fourth term:
fourth term = (third term) + (common difference)
= (-8/15) + (-3/5)

To add fractions, you need to have a common denominator. In this case, the common denominator is 15.

fourth term = (-8/15) + (-9/15)
= -17/15
= -1 2/15 (mixed number)

Finally, to find the fifth term:
fifth term = (fourth term) + (common difference)
= (-1 2/15) + (-3/5)

To find the sum of a mixed number and a fraction, you need to convert the mixed number to an improper fraction.

fifth term = (-17/15) + (-9/15)
= -26/15
= -1 11/15 (mixed number)

Therefore, the next three terms of the arithmetic sequence are: -8/15, -17/15, and -1 11/15.