A website Maths Puzzle Numerical Ability

The seventh common term between the series 3+7+11+... and 1+6+11+.. is?

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Geometric problem (which will be described via words, unfortunately)

Points A, B, and C lie on the diameter of a semi-circle, with points A and C at the perimeter of the semi-circle. Point B lies along the diameter 4cm from point A and 1cm from point B. At point B, a perpendicular is drawn, and where it intersects the perimeter of the semi-circle is point D.

What is the distance between points B and D?
the owner of the mansion has been murdered .the visitors to the mansion were alex, balu and chandru. who was the murderer?