등비수열 홀수항 합

$a _{n}$이 등비수열이므로 $a _{3} = 4 ( a _{2} - a _{1} )$에서 $ar ^{2} = 4 ( ar - a )$ $r ^{2} = 4 r - 4$ $( r - 2 ) ^{2} = 0$ $\therefore r = 2$ $\displaystyle \sum\limits _{k = 1} ^{6} a _{{} _{k}} = \frac{a ( 1 - r ^{6} )}{1 - r} = 15$ 에서 $\displaystyle a = \frac{15}{63} = \frac{5}{21}$ 따라서 $a _{1} + a _{3} + a _{5}$$= a + ar ^{2} + ar ^{4}$$= a ( 1 + r ^{2} + r ^{4} )$ $\displaystyle = \frac{5}{21} ( 1 + 2 ^{2} + 2 ^{4} )$$= 5$