2. consider the sequence –8, 4, -2, 1, -1/2, … ( it is a geometric sequence)

e) find the tenth term in the sequence. show all your work.

The nth term of any geometric sequence can be expressed as:

a(n)=ar^(n-1), a(n)=nth term, a=initial term, r=common ratio, n=term number...

We can easily see that the first term, a=-8

The common ratio is 4/-8=-2/4=1/-2=r=-1/2 so the rule is:

a(n)=-8(-1/2)^(n-1) so the tenth term is:

a(10)=-8(-1/2)^(10-1)

a(10)=-8(-1/2)^9

a(10)=1/64