Question

give two arithmetic means between 6 and 21

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

Two arithmetic means between 6 and 21

CALCULATION

Let x and y be two arithmetic means between 6 and 21

Then 6 , x, y, 21 forms an Arithmetic progression

Here first term = 6

Let Common Difference = d

So

$\sf{ \: x = 6 + d \: }$

$\sf{ \: y = 6 + 2d \: }$

$\sf{ \: 21 = 6 + 3d \: }$

Now

$\sf{ \: 21 = 6 + 3d \: } \: \: gives$

$\sf{ \: 6 + 3d = 21 \: }$

$\implies \: \sf{ \: 3d = 15\: }$

$\implies \: \sf{ \: d = 5\: }$

So

$\: \sf{ \: x = 6 + 5 = 11\: }$

$\: \sf{ \: y = 6 +(2 \times 5 ) = 6 + 10 = 16\: }$

Hence the two arithmetic means between 6 and 21 are 11 , 16

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