$13, 25, 61, 121, 205, (?)$

Find out the odd number from the given sequence: $5, 6, 16, 57, 246, 1245, 7506$.

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?

$4, 10, ?, 82, 244, 730$

Find the odd number in the given sequence: $864, 420, 200, 96, 40, 16, 6$.

Find the odd number from the given sequence: $24, 18, 222, 82, 421$.