Question

Insert five arithmetic means between 14 and86​

Answer 1

The five arithmetic means between 14 and 86 are 26,38,50,62,74

Explanation:

We need to find five arithmetic means between 14 and 86

The formula used to find arithmetic mean is:
`a_(n)=a_(1) +(n-1)d`

Where n is the number of terms and d is the common difference

We are given 1st and 7th term.

Using 7th term to find value of d

`a_(n)=a_(1) +(n-1)d\\a_(7)=14 +(7-1)d\\86=14+6d\\86-14=6d\\72=6d\\d=(72)/(6)\\d=12`

So, difference between each term d is 12

Now finding five arithmetic terms i.e a₂, a₃, a₄, a₅, a₆

Using the formula
`a_(n)=a_(1) +(n-1)d` to find terms

Finding term a₂

`a_(n)=a_(1) +(n-1)d\\a_(2)=14 +(2-1)12\\a_(2)=14 +12\\a_(2)=26`

Finding term a₃

`a_(n)=a_(1) +(n-1)d\\a_(3)=14 +(3-1)12\\a_(3)=14 +2*12\\a_(3)=38`

Finding term a₄

`a_(n)=a_(1) +(n-1)d\\a_(4)=14 +(4-1)12\\a_(4)=14 +3*12\\a_(4)=50`

Finding term a₅

`a_(n)=a_(1) +(n-1)d\\a_(5)=14 +(5-1)12\\a_(5)=14 +4*12\\a_(5)=62`

Finding term a₆

`a_(n)=a_(1) +(n-1)d\\a_(6)=14 +(6-1)12\\a_(6)=14 +5*12\\a_(6)=74`

So, the five arithmetic means between 14 and 86 are 26,38,50,62,74