Question

The average of first 3 numbers of 7 consective natural numbers is 15 and average of lasf 3 numbers.is 19 which are the 7 consective natural numbers.?

Answer 1

Answer:

14, 15, 16, 17, 18, 19 and 20

Step-by-step explanation:

Let the 7 consecutive natural numbers be n-3, n-2, n-1, n, n+1, n+2 and n+3

Given

The average (mean) of the first 3 numbers of these 7 numbers i.e., n-3, n-2, and n-1 is 15.

⇒ (n-3 + n-2 + n-1)/3 = 15  [∴Mean = sum of observations / Total no. of

                                            observations]

⇒3n - 6 = 15*3

⇒3(n - 2) = 15*3

⇒n - 2 = 15*3/3

⇒n - 2 = 15

∴n = 15 + 2

∴n = 17

Similarly if we solve the second case i.e., finding average for n+1, n+2 and n+3 we will also get n = 17

∴The 7 consecutive numbers = n-3, n-2, n-1, n, n+1, n+2, n+3

                                                 = 17-3, 17-2, 17-1, 17, 17+1, 17+2, 17+3

                                                 = 14, 15, 16, 17, 18, 19 and 20.