The sequence c1,C2, C3, ... defined by the equations C1 = 0,Cn = 4c|n| + n for all integer n>1 %3D a) Compute c1, C2, C3, C4 and c5 (n+1)2 b) Prove that 8 < Cn for all integer n 2 2. (Hint: 2 for all n)

I'm not sure where to begin with setting up this equation please help.

A length of wire that is 160 cm long is cut into two pieces: one to form an equilateral triangle and the other to form a circle. Where do you cut the wire to makes shapes that enclose a maximum amount of area for the two shapes? Where do you cut the wire to enclose a minimum amount of area for the two shapes?

A fence is to be built to enclose a rectangular area of 300 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material along the fourth side costs 12 dollars per foot. Find the length and width of the enclosure that is most economical to construct.