Question

What is the 10th term 1,
1/2,1/4

Answer 1

Answer:

The 10th term will be:

                                                         $a_{10}=\frac{1}{512}$

Step-by-step explanation:

Considering the sequence

$1,\:\frac{1}{2},\:\frac{1}{4}...$

A geometric sequence has a constant ratio r and is defined by

$a_n=a_0\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{\frac{1}{2}}{1}=\frac{1}{2},\:\quad \frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=\frac{1}{2}$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=1$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=\left(\frac{1}{2}\right)^{n-1}$

Putting n = 10 to determine in the nth term to determine the 10th term

$a_{10}=\left(\frac{1}{2}\right)^{10-1}$

$a_{10}=\left(\frac{1}{2}\right)^9$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$a_{10}=\frac{1^9}{2^9}$

$a_{10}=\frac{1}{2^9}$     ∵ $1^9=1$

$a_{10}=\frac{1}{512}$     ∵  $2^9=512$

Therefore, the 10th term will be:

                                                         $a_{10}=\frac{1}{512}$