Question

Insert 3 arithmetic means between -8 and 32.
-8,_,_,_,32
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Answer 1

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Answer 2

SOLUTION

TO DETERMINE

Insert 3 arithmetic means between - 8 and 32.

CONCEPT TO BE IMPLEMENTED

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

EVALUATION

Let x , y , z are 3 arithmetic means between - 8 and 32.

Then - 8 , x , y , z , 32 are in Arithmetic Progression

First term = a = - 8

Let common difference = d

x = - 8 + d

y = - 8 + 2d

z = - 8 + 3d

32 = - 8 + 4d

Now we have

- 8 + 4d = 32

⇒ 4d = 40

⇒ d = 10

Thus we have

x = - 8 + d = - 8 + 10 = 2

y = - 8 + 2d = - 8 + 20 = 12

z = - 8 + 3d = - 8 + 30 = 22

FINAL ANSWER

Hence 3 arithmetic means between - 8 and 32 are 2 , 12 , 22

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