Question

Insert five arithmetic means between 14 and86​

Answer 1

Answer:

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

Step-by-step 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

$a_{n}=a_{1} +(n-1)d\\a_{7}=14 +(7-1)d\\86=14+6d\\86-14=6d\\72=6d\\d=\frac{72}{6}\\d=12$

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