주기 수열의 합

$a _{1} = 2$ $a _{2} = 2 \times a _{1} - 1 = 2 \times 2 - 1 = 3$ $a _{3} = 2 \times a _{2} - 1 = 2 \times 3 - 1 = 5$ $a _{4} = 2 \times a _{3} - 1 = 2 \times 5 - 1 = 9$ $\displaystyle a _{5} = \frac{1}{3} \times a _{4} = \frac{1}{3} \times 9 = 3 = a _{2}$ $a _{6} = a _{3}$ $a _{7} =$$a _{4}$ $\vdots$ $a _{n + 3} = a _{n} \left( n \geq 2 \right)$이므로 $\displaystyle \sum\limits _{k = 1} ^{16} a _{k}$$= a _{1} + \left( a _{2} + a _{3} + a _{4} \right) + \cdots + \left( a _{14} + a _{15} + a _{16} \right)$ $= 2 + ( 3 + 5 + 9 ) \times 5 = 87$