Step-by-step explanation:
There is a common difference between successive terms:
3/5 - 2/3 = 9/15 - 10/15 = -1/15
8/15 - 3/5 = 8/15 - 9/15 = -1/15
7/15 - 8/15 = -1/15
So the sequence is arithmetic with a common difference d = -1/15. The recursive and explicit forms are:
an = an-1 + d = an-1 - 1/15
an = a1 + (n-1)d = 2/3 - (n-1)/15
You want to find the next term in the sequence, which is the 5th term so n=5. Use the recursive form:
a5 = a4 - 1/15
where a4 = the fourth term in the sequence.
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Answers & Comments
Step-by-step explanation:
There is a common difference between successive terms:
3/5 - 2/3 = 9/15 - 10/15 = -1/15
8/15 - 3/5 = 8/15 - 9/15 = -1/15
7/15 - 8/15 = -1/15
So the sequence is arithmetic with a common difference d = -1/15. The recursive and explicit forms are:
an = an-1 + d = an-1 - 1/15
an = a1 + (n-1)d = 2/3 - (n-1)/15
You want to find the next term in the sequence, which is the 5th term so n=5. Use the recursive form:
a5 = a4 - 1/15
where a4 = the fourth term in the sequence.