How do you find the indicated term of the geometric sequence where #a_4=16#, r=0.5, n=8?

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Answer 1 · 2017-04-19T09:18:41

#a_8=1#. See explanation.

In the given sequence we have:

#a_4=16#, #r=1/2#

This is a geometric sequence, so we can write that:

#a_{n+1}=a_n*r#

Using this identity we get:

#a_5=a_4*r#

#a_6=a_5*r=a_4*r^2#

#a_7=a_6*r=a_4*r^3#

#a_8=a_7*r=a_4*r^4#

If we substiute the given values we get:

#a_8=16*(1/2)^4=16*1/16=1#

Answer: The eighth term of this sequence is #a_8=1#.