Question

Find the five arithmetic means between -2 and 16.
Answer

1, 4, 7, 11, 14

1, 3, 6, 9, 12

1, 4, 7, 10, 13

0, 3, 7, 10, 13

Answer 1

a, x₁, x₂, x₃,.....x_n, b are in are in arithmetic progression.

Where x₁, x₂, x₃,.....x_n are arithmetic means between a and b.

Common difference d = (b - a)/(n + 1)

Arithmetic mean between - 2 and 16

In this case a = - 2, b = 16 and n = 5

-2, x₁, x₂, x₃, x_4, x₅, 16

 d = [16 - (- 2)]/(5 + 1)

= 18/6

d = 3

 

Arithmetic progression a, a+d, a+2d, a+3d, a+4d, a+5d, a+ 6d.

a = -2 and a + 6d = 16

Add 3 to every term.

x₁ = - 2 + 3 = 1

x₂ = 1 + 3 = 4

x₃ = 4 + 3 = 7

x₄ = 7 + 3 = 10

x₅ = 10 + 3 = 13

The five arithmetic means between - 2 and 16 are 1, 4, 7, 10, 13.

Option 3 is correct.