Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

Find the sum to n terms in the geometric progression 1,-a, a²,-a³, ... (if a ≠ -1)

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)thnumbers is 5:9. Find the value of m.

Find the 20th and nthterms of the G.P.

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.