question and answers of number theory

Question 1 - Question: For the given sequence, suggest possible next three terms and find the general term. 7, 11, 15,---- Answer: First term = 7, Common Difference = 11 - 7 = 15 - 11 = 4 Next three terms are 15 + 4 = 19, 19 + 4 = 23, 23 + 4 = ..

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Question 1 - Question: Define an even number. Answer: A number which is divisible by 2 is called an even number..

Scientific Notation - Notation of large number in terms of exponential form, 10 raised to required value. It is also a standart notation representation as " p x 10 q ". where 'p' and 'q' are any integer..

Let n(R) = number of boys of who play rugby n(T) = number of boys who play tennis Let x = number of boys who play both the games From the above diagram it is clear that, Those who play rugby only = 60 - x = 60 - 15 = 45 Those who play tennis only = 35 - 15 =..

Let x be the third proportional to 5 and 10. 5:10=10:x. 5x=10 x 10 (product of extreme is equal to product of means) 6) Find two numbers such that the mean proportional between them is 24 and the third proportional to them is 19..

= (14 - 12) - (7 - 3) + (4 - 2) = 2 - 4 + 2 = 0 The system may have infinite number of solutions or no solution. Put x = k in (1) and (2) and solve y + z = 6 - k 2y + 3z = 14 - k. Solving the above two equations, we have z = k + 2 and y = 4 - 2k When x = k, substituting these value..

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..

3. To find the sum to the cubes of first n natural numbers. ..