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

Apr 19, 2017

${a}_{8} = 1$. See explanation.

#### Explanation:

In the given sequence we have:

${a}_{4} = 16$, $r = \frac{1}{2}$

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

${a}_{n + 1} = {a}_{n} \cdot r$

Using this identity we get:

${a}_{5} = {a}_{4} \cdot r$

${a}_{6} = {a}_{5} \cdot r = {a}_{4} \cdot {r}^{2}$

${a}_{7} = {a}_{6} \cdot r = {a}_{4} \cdot {r}^{3}$

${a}_{8} = {a}_{7} \cdot r = {a}_{4} \cdot {r}^{4}$

If we substiute the given values we get:

${a}_{8} = 16 \cdot {\left(\frac{1}{2}\right)}^{4} = 16 \cdot \frac{1}{16} = 1$

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