Show that the products of the corresponding terms of the sequences a,ar,ar², ...ar^n-1 and A, AR, AR², ,,,AR^n-1 form a G.P, and find the common ratio.

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.

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio 

The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 …

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

A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P²Rⁿ = Sⁿ

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