Question

4. Insert three arithmetic means between 11 and 35​

Answer 1

Question :-

→ Insert three arithmetic means between 11 and 35_??

Answer :-

→ Given :

→ a = 11

→ a5 = 3

→ Common Difference :

→ d = ( as -a ) / ( 5 - 1 ) d

→ = ( 35 - 11 ) / 4 d

→ = 24 / 4

→ d = 6

→ Arithmetic Means :

→ a2 = a + d a2

→ = 11 + 6 a2

→ a3 = 17

→ = a1 + 2d a3

→ = 11 + 2 ( 6 ) az

→ = 23 24

→ = a1 + 3d 24

→ = 11 + 3 ( 6 )

→ a4 = 29

So ,

The 3 numbers between 11 and 35 are 6 , 17 and 29 .

Answer 2

SOLUTION

TO DETERMINE

Insert 3 arithmetic means between 11 and 35

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 11 and 35

Then 11 , x , y , z , 35 are in Arithmetic Progression

First term = a = 11

Let common difference = d

x = 11 + d

y = 11 + 2d

z = 11 + 3d

35 = 11 + 4d

Now we have

11 + 4d = 35

⇒ 4d = 24

⇒ d = 6

Thus we have

x = 11 + d = 11 + 6 = 17

y = 11 + 2d = 11 + 12 = 23

z = 11 + 3d = 11 + 18 = 29

FINAL ANSWER

Hence 3 arithmetic means between 11 and 35 are 17 , 23 , 29

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