Select the missing number from the following options to complete the given series:
$$15,5,30,25,90,150,360,\_\_\_,1800,8400$$

The given series consists of two interleaved alternating series:
Series 1 (Odd-indexed positions):
$1^{\text{st}}$ term = $15$
$3^{\text{rd}}$ term = $15\times 2=30$
$5^{\text{th}}$ term = $30\times 3=90$
$7^{\text{th}}$ term = $90\times 4=360$
$9^{\text{th}}$ term = $360\times 5=1800$
(Pattern: multiply by $2,3,4,\mathrm{5...}$)

Series 2 (Even-indexed positions):
$2^{\text{nd}}$ term = $5$
$4^{\text{th}}$ term = $5\times 5=25$
$6^{\text{th}}$ term = $25\times 6=150$
$8^{\text{th}}$ term (Missing term) = $150\times 7=1050$
$10^{\text{th}}$ term = $1050\times 8=8400$
(Pattern: multiply by $5,6,7,\mathrm{8...}$)

The missing term is the $8^{\text{th}}$ position, which is $150\times 7=1050$.