Tuesday, May 5, 2015

`a_1 = 5/8, a_(n + 1) = a_n - 1/8` Write the first 5 terms of the sequence defined recursively.

The given recursive formula of the sequence is:


`a_1=5/8`


`a_(n+1)=a_n-1/8`


To solve for the second term, plug-in n=1 and `a_1=5/8` .


`a_(1+1)=a_1 - 1/8`


`a_2=5/8-1/8=4/8=1/2`


To solve for the third term, plug-in n=2 and `a_2=1/2` .


`a_(2+1)=a_2-1/8`


`a_3=1/2-1/8=4/8-1/8=3/8`


To solve for the fourth term, plug-in n=3 and `a_3=3/8` .


`a_(3+1)=a_3-1/8`


`a_4=3/8-1/8=2/8=1/4`


To solve for the fifth term, plug-in n=4 and `a_4=1/4` .


`a_(4+1)=a_4-1/8`


`a_5=1/4-1/8=2/8-1/8=1/8`


Therefore, the first five terms of the sequence are `{5/8, 1/2, 3/8,1/4,1/8, ...}` .

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