Question

Find five arithmetic means between 1and 19

Answer 1

Given,

first term (a) = 1

last term (l) = 19

let the five arithmetic mean between 1 and 19 be A₁, A₂, A₃, A₄, A₅

Now,

1, A₁, A₂, A₃, A₄, A₅, 19 are in AP

Number of terms(n)= 5+2 = 7

We know tha last term of AP is given by,

l = a + (n-1)d ( where d is common differecne between the terms)

19 = 1 + (7-1)d

19 = 1 + 6d

18= 6d

d= 3

Again,

A₁ = a + (2-1)d ( as A₁ is second term of AP)

A₁ = 1 + 3

A₁ = 4

Similarly

A₂ = a + 2d

A₂ = 1 + 6

A₂ = 7

A₃ = a + 3d

A₃ = 1 + 3*3

A₃ = 10

A₄ = a + 4d

A₄ = 1 + 4*3

A₄ = 13

A₅ = a + 5d

A₅ = 1 + 5*3

A₅ = 16