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These can be inserted between a and b. b. To find the sum of n arithmetic means between the two given quantities: Let the two quantities (numbers) be a and b. The required sum = A 1 + A 2 + A 3 + ---- + A..

Question: Find three numbers in AP whose sum is 33 and whose product is 1155. Answer: Let a - d, a, a + d be the three numbers in AP. The numbers are ..

Step 1: Factor pairs of the last term are (-7,+3), (21,-1), (+7,-3), (-21,+1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (+7,-3). Step3: Rewrite the expression using these factors as w 2 + 7w - 3w -21. Step 4: Group the terms and factorise...

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..

The theory of finite sets is, arguably, a definition of Combinatorics. In particular, certain combinatorial topics (e.g. Ramsey theory) have important direct analogues in "combinatorial" set theory. Since Axiomatic Set Theory is often used to construct the natural numbers ..

Geometric Progressions (G.P.) - The series of terms a, ar, ar 2 , ar 3 ,.... in which each term bears a constant ratio to the preceeding term is a geometric progression. The constant ratio is called the common ratio.OR A geometrical progression is a succession of terms such that each term bears fix..

.02 cm. The unit of accuracy required is hundredth of a centimeter. Therefore, only digit 2 is significant. The 0 after decimal indicates the magnitude of measurement. Therefore, the 0 after decimal point is not significant. .02 cm has one significant figure. To sum up the above examples:..

The sum and product of two conjugate numbers is always real. 2a + i(0) 2a ..

2. Find the sum to n terms of the seri..

Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matr..