An arithmetic progression is a sequence of numbers in which the distance (or difference) between any two successive numbers if the same. this in the sequence 1, 3, 5, 7, the distance is 2 while in the sequence 6, 12, 18, 24, the distance is 6. given the positive integer distance and the positive integer n, associate the variable sum with the sum of the elements of the arithmetic progression from 1 to n with distance distance. for example, if distance is 2 and n is 10, then sum would be associated with 25 because 1+3+5+7+9 = 25.

5.a fishing rod is formed from a composite material of 0.5 kg of glass fibers embedded in a matrix of 0.5 kg of epoxy resin. the glass fibers are assumed to be long, continuous and unidirectional. to achieve a greater stiffness it is proposed to use a different composite that is comprised of long continuous carbon fibers that will be embedded in a matrix of 0.5 kg of epoxy resin. if the modulus of elasticity of the carbon fiber composite is 10% greater than the elastic modulus of the glass fiber composite, estimate the mass of carbon fibers that will be used to make the carbon fiber composite. assume the applied tensile stress is parallel to the direction of the long axis of the fibers. the epoxy resin, glass fiber, and carbon fiber have an elastic modulus of 5, 86, and 350 gpa respectively and a density of 1100, 2500, and 1800 respectively.