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1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, b-k, c-k are in A.P...

1, 3, 5, 7..... (adding 2 to every term) 1, 4, 16, 64 (Multiplying by 4 every term) 20, 17, 14 . (add -3 to every term) The different numbers in a sequence are called terms of sequence. The subscripts denote the position of the term. In the second example, 4 i..

Question: From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, including atleast 4 boys and 4 girls. 2 girls who won prizes last year should be included. In how many ways the selection can be made? Answer: There are 12 boys and 10 gir..

Using matrix method, solve the following system of linear equations x + y + z = 6 (1) x + 2y + 3z = 14 (2) x + 4y + 7z = 30 ..

Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the sum of the series...

1. To find the sum of first n natural numbers. 2. To find the sum to squares of first n natural numbers. 3. To find the sum to the cubes of first n natural numbers. 4. Method of finding sum of a series whose nth term is know..

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...

Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..

8! = 8 x 7 x 6 x 5 x4 x 3 x 2 x 1 = 40320 ..

Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..