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Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..

Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..

A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..

n t h term of (1,2,3,....) is n Subtracting (ii) from (i), we get ..

Question 1 - Question: Find n. Answer: ..

Arithmetic Geometric Series - A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..

Question: When n = 5 and r = 2, find the values of Answer: i) ii) ..

Question: Answer: = 5 + 10 + 10 + 5 + 1 = 31 = RH..

We have already learnt in the previous class that the area of triangle whose vertices are (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ) is given by Hence area of a triangle having vertices at (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) is given by..

Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...