Question

Insert four arithmetic means between 4 and 29.​

Answer 1

let them be

4, 4+d, 4+2d, 4+3d, 4+4d, 25

clearly 29 = 4 + 5d

5d = 29 - 4 = 25

d = 25/5

d = 5

4, 9, 14, 19, 24, 29

Answer 2

SOLUTION

TO DETERMINE

Insert four arithmetic means between 4 and 29.

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 , u are four arithmetic means between 4 and 29.

Then 4 , x , y , z , u , 29 are in Arithmetic Progression

First term = a = 4

Let common difference = d

x = 4 + d

y = 4 + 2d

z = 4 + 3d

u = 4 + 4d

29 = 4 + 5d

Now we have

4 + 5d = 29

⇒ 5d = 25

⇒ d = 5

Thus we have

x = 4 + d = 4 + 5 = 9

y = 4 + 2d = 4 + 10 = 14

z = 4 + 3d = 4 + 15 = 19

u = 4 + 4d = 4 + 20 = 24

FINAL ANSWER

Hence four arithmetic means between 4 and 29 are 9 , 14 , 19 , 24

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