Q : 5 A small terrace at a football ground comprises of steps each of which is m long and built of solid concrete. Each step has a rise of and a tread of . (see Fig. ). Calculate the total volume of concrete required to build the terrace.
[Hint : Volume of concrete required to build the first step ]
Q : 4 The houses of a row are numbered consecutively from to . Show that there is a value of such that the sum of the numbers of the houses preceding the house numbered is equal to the sum of the numbers of the houses following it. Find this value of . [Hint : ]
Q : 3 A ladder has rungs cm apart. (see Fig. ). The rungs decrease uniformly in length from cm at the bottom to cm at the top. If the top and the bottom rungs are m apart, what is the length of the wood required for the rungs?
[Hint : Number of rungs
Q : 2 The sum of the third and the seventh terms of an AP is and their product is . Find the sum of first sixteen terms of the AP.
Q : 1 Which term of the AP : is its first negative term? [Hint : Find for ]