Question

The sum of 3 AM between a and 22 is 42 then a:

Answer 1

The sum of 3 AM between a and 22 is 42 then a is 6

Solution:

Given, the sum of 3 AM between a and 22 is 42  

Then we have to find the “a” value.

Now, we know that, common difference of n AMs between a and b $=\frac{b-a}{n+1}$

Here, a = a and b = 22. And n = 3.

$\text { Then, common difference }=\frac{22-a}{3+1}=\frac{22-a}{4}$

$\text { Then, the } 3 \text { AMs are } a+\frac{22-a}{4}, a+2\left(\frac{22-a}{4}\right), a+3\left(\frac{22-a}{4}\right)$

We know that, sum of 3 AMs = 42

$\text { Then, } a+\frac{22-a}{4}+a+2\left(\frac{22-a}{4}\right)+a+3\left(\frac{22-a}{4}\right)=42$

$3 a+6\left(\frac{22-a}{4}\right)=42$

12a + 6(22 – a) = 42 x 4  

12a + 132 – 6a = 168

6a = 168 – 132

6a = 36

a = 6.

Hence, the value of a is 6.

Answer 2

The sum of 3 AM between a and 22 is 42 then a = 6

Step-by-step explanation:

Let say 5 terms including 3 AM between a & 22 are

a  a + d , a+2d  , a + 3d  , a + 4d

a + 4d = 22

a + d + a + 2d + a + 3d = 42

=> 3a + 6d = 42

Dividing by 3

=> a + 2d = 14

=> (a + 4d) - (a + 2d) =  22 - 14

=> 2d = 8

=> d = 4

a + 2 d = 14

=> a + 2 * 4 = 14

=> a + 8 = 14

=> a = 6