Question
If {(tanx)/(secx)} × cosx = (1/2), then determine the
value of ‘sin2x’.Solution

The question below is based on the given series I. The series I satisfy a certain pattern, follow the same pattern in series II and answer the question...
3, 49, 191, 477, ?, 1673
What will be the next number in the series?
2,5,11,23,47,?
38    40    83    254    ?     5126
24 47 137 ? 2679 16049
...10 625 50 125 250 25 ?
...[(288)2 ÷ 96 × ?] ÷ 44 = 432
1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...
3, 4, 10, 33, 136, ?, 4116
77 ? 190 257 331 412
...