Question

1. the sum of the first n odd positive integers is 64. what is the value of n ?

Answer 1

• The value of the n is 8.
• There are 7 positive integers between 100 and 200 which are divisible by 14.

Step-by-step explanation:

The sum of first n odd positive integer is n^2. The nth odd number is 2n-1.

                          i.e. 1 + 3 + ........+ (2n-1) = n^2.  

                                1 + 3 +..........+ (2n-1) = 64

                                                                n^2 = 64

                                                                    n = 8.

The positive integers between 100 and 200 which are divisible by 14 are 112, 126, 140, 154, 168, 182, 196. It is obtained by the multiples of 14 between 100 and 200.

100 = 7 * 14 + 2

200 = 14 * 14 + 4. The answer is 14 - 7 = 7

The seven numbers are

                        14 * 8 = 112

                        14 * 9 = 126

                        14 * 10 = 140

                        14 * 11 = 154

                        14 * 12 = 168

                        14 * 13 = 182

                        14 * 14 = 196