In the multiplication table made earlier, take a.square of nine numbers, instead of four, and mark the numbers at the four corners:
i) What is the. difference of diagonal sums? ii) Explaín using algebra, why this différence is the same for all such squares. iii) Whaț jf we take a square of sixteen numbers?

i) In a calendar, a square of four. numbers is marked. The sum of the numbers is 80. What are the numbers? ii) A square of nine numbers is marked in a calendar. The sum of all these numbers is 90. What are the numbers?

Write each of the operations below as algebraic expressions, find out which are polynomials and explain why. i) Sum of a number and its reciprocal. ii) Sum of a number and its square root. iii) Product of the sum and difference of a number and its square root.

Consider all rectangles that can be made with a 1m long rope. Take one of its side as x cm and the area enclosed as a(x) sq.cm. i) Write the relation between a(x) and xas in equation ii) Why are the numbers a(10) and a(40) equal? iii) To get the same number as a(x), for two different numbers as x, what must be the relation between the numbers?

Check whether each of the sequences given below is ah arithmetic sequence, give reaśons. For the arithmetic 'sequences, write the common difference also. i) Sequence of natural numbers ii) Sequence of multiples of three iii) Sequence of prime numbers, iv) Sequence of square numbers v) Sequence of powers of three