The sum of first n terms of a certain series is given as 2n² - 3n.Show that the series is an A.P

In a G.P. the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is \(\frac { 57 }{ 2 } \). Find the three terms.

If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of G.P then prove that x^b-c x y^c-a x z^a-b = 1

A person saved money every year, half as much as he could in the previous year. If he had totally saved Rs.7875 in 6 years then how much did he save in the first year?

If 1³ + 2³ + 3³+...k³ = 44100 then find 1 + 2 + 3 +...+ k

Find the sum of the series (2³- 1) + (4³ - 3³) + (6³ - 15³)+....to (i) n terms,  (ii) 8 terms

A milk man has 175 litres of cow’s milk and 105 litres of buffalo’s milk. He wishes to sell the milk by filling the two types of milk in cans of equal capacity. Calculate the following (i) Capacity of a can (ii) Number of cans of cow’s milk (iii) Number of cans of buffalo’s milk.

A man saved Rs.16500 in ten years. In each year after the first he saved Rs.100 more than he did in the preceding year. How much did he save in the first year?

Find the sum of
5² + 10² + 15² +...+ 105²

Raghu wish to buy a laptop. He can buy it by paying Rs. 40,000 cash or by giving it in 10 installments as Rs. 4800 in the first month, Rs. 4750 in the second month, Rs. 4700 in the third month and so on. If he pays the money in this fashion, find how much extra amount that he has to pay than the cost?