Question

Insert three arithmetic means between 11 and 19.

Answer 1

Answer:

13, 15 and 17

Step-by-step explanation:

let 3 arithmetic mean be p-d , p and p+d,

then,

a = 11

common difference = p-d-11 = p-(p-d) and p+d-p = 19-(p+d)

p-d-11 = p-p+d

p-2d = 11 ----(I)

p+d-p = 19-p-d

p+2d = 19 ---(ii)

from equation (I) and (ii),

p-2d = 11

p+2d = 19

2p = 30

p = 15

on putting value, we get,

p-2d = 11

15-2d = 11

2d = 4

d = 2

p-d = 15-2 = 13

p+d = 15+2 = 17