Question #42911

Jul 10, 2016

${T}_{12} = \frac{1}{1024} , \text{ " T_15 = 1/8192," } {T}_{20} = \frac{1}{262144}$

Explanation:

This is a geometric sequence.

Each term is half of the preceding term, so the
common ratio, "r" = $\frac{1}{2}$

The First term, "a" = 2.

The sequence can therefore be defined by its general term:

${T}_{n} = a {r}^{n - 1} \text{ } \Rightarrow 2 \times {\left(\frac{1}{2}\right)}^{n - 1}$

This will simplify to ${T}_{n} = {\left(\frac{1}{2}\right)}^{n - 2}$

${T}_{12} = {\left(\frac{1}{2}\right)}^{10} = \frac{1}{1024}$

${T}_{15} = {\left(\frac{1}{2}\right)}^{13} = \frac{1}{8192}$

${T}_{20} = {\left(\frac{1}{2}\right)}^{18} = \frac{1}{262144}$