INSERTING ARITHMETIC MEANS BETWEEN TWO NUMBERS

Problem 1 :

Insert 4 arithmetic mean between 4 and 324.

Solution :

Let first term a = 4, and last term = 324

4, __, __, __, __, 324

a = 4, a + d, a + 2d, a + 3d, a + 4d are unknowns

a + 5d = 324

Applying the vale of a, we get

4 + 5d = 324

5d = 324 - 4

5d = 320

d = 320/5

d = 64

So, the four arithmetic means are 68, 132, 196 and 260.

Problem 2 :

The two arithmetic means between -6 and 14 is

a)  2/3, 1/3      b)  2/3, 7 1/3       c)  -2/3, -7  1/3    d)  none

Solution :

Let first term a = -6, and last term = 14

-6, __, __, 14

a = -6, a + d, a + 2d are unknowns

a + 3d = 14

Applying the vale of a, we get

-6 + 3d = 14

3d = 14 + 6

3d = 20

d = 20/3

a + d ==> -6 + (20/3)

= (-18 + 20)/3

= 2/3

a + 2d ==> -6 + 2(20/3)

= (-18 + 40)/3

= 22/3 or 7  1/3

So, the answer is option b.

Problem 3 :

The 4 arithmetic means between -2 and 23 are

a) 3, 13, 8, 18     b)  18, 3, 8, 13

c)  3, 8, 13, 18       d) none 

Solution :

Let first term a = -2, and last term = 23

-2, __, __, __, __, 23

a = -2, a + d, a + 2d, a + 3d, a + 4d are unknowns

a + 5d = 23

Applying the value of a, we get

-2 + 5d = 23

5d = 23 + 2

5d = 25

d = 5

So, the solution is 3, 8, 13, 18, option c.