$2, 3, 3, 5, 10, 13, ?, 43, 172, 177$

$16, 22, 40, 78, 144, ?$

$7, 11, 23, 51, 103, (?)$

What is the value of $S = \frac{1}{1 \times 3 \times 5} + \frac{1}{1 \times 4} + \frac{1}{3 \times 5 \times 7} + \frac{1}{4 \times 7} + \frac{1}{5 \times 7 \times 9} + \frac{1}{7 \times 10} + \dots$ up to $20$ terms?

$123 \quad 140 \quad 106 \quad 157 \quad 89 \quad ?$

Find the missing number in the series: $15, 20, 30, ?$