Question

Insert six arithmetic mean between 2 and 16.Also prove that their sum is 6 times the A.M between 2 and 16​

Answer 1

Given : Number 2 and 16

To Find :   six arithmetic mean  in between

prove that their sum is 6 times the A.M between 2 and 16​

Solution:

Number 2 and 16

if 6 AMs are inserted in between

then total numbers will be 2 + 6 = 8

16 = 2 + (8 - 1)d

=> 14 = 7d

=> d = 2

so AP is

2 , 4 , 6 , 8 , 10 , 12 , 14 , 16

Hence 6 AM

4 , 6 , 8 , 10 , 12 , 14

Sum of AM = 4 + 6 + 8 + 10 + 12 + 14  =  54

AM of 2 and 16 = (2 + 16)/2 = 9

9 x 6  = 54

their sum is 6 times the A.M between 2 and 16​

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