How do you find the indicated term of the geometric sequence where $a_{4} = 16$ $a_4=16$ , r=0.5, n=8?

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Answer 1 · 2017-04-19T09:18:41

$a_{8} = 1$ $a_8=1$ . See explanation.

In the given sequence we have:

$a_{4} = 16$ $a_4=16$ , $r = \frac{1}{2}$ $r=1/2$

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

$a_{n + 1} = a_{n} \cdot r$ $a_{n+1}=a_n*r$

Using this identity we get:

$a_{5} = a_{4} \cdot r$ $a_5=a_4*r$

$a_{6} = a_{5} \cdot r = a_{4} \cdot r^{2}$ $a_6=a_5*r=a_4*r^2$

$a_{7} = a_{6} \cdot r = a_{4} \cdot r^{3}$ $a_7=a_6*r=a_4*r^3$

$a_{8} = a_{7} \cdot r = a_{4} \cdot r^{4}$ $a_8=a_7*r=a_4*r^4$

If we substiute the given values we get:

$a_{8} = 16 \cdot {(\frac{1}{2})}^{4} = 16 \cdot \frac{1}{16} = 1$ $a_8=16*(1/2)^4=16*1/16=1$

Answer: The eighth term of this sequence is $a_{8} = 1$ $a_8=1$ .

How do you find the indicated term of the geometric sequence where a_4=16a4=16a_4=16, r=0.5, n=8?