Question

insert 8 arithmetic means between -1 and 2 verify that their sum is 8 times single arithmetic mean between them​

Answer 1

Given  : - 1  and  2

To Find : insert 8 arithmetic means

verify that their sum is 8 times single arithmetic mean between them​

Solution:

- 1  and  2

single arithmetic mean = ( - 1 + 2)/2  = 1/2

8 arithmetic means  to be inserted

Hence total numbers = 10

a = - 1

L = 2

n = 10

2  = - 1  + (10 -1)d

=> 3 = 9d

=> d = 3/9

=> d = 1/3

8 arithmetic means

-1 + 1/3  ,  - 1 + 2(1/3) , - 1 + 3(1/3) , - 1 + 4(1/3) , - 1 + 5(1/3), - 1 + 6(1/3) , - 1 + 7(1/3) , - 1+ 8(1/3)

= -2/3  ,  - 1/3 , 0 , 1/3 , 2/3 ,  1 , 4/3  , 5/3

Sum =    4

= 8(1/2)

= 8 times single arithmetic mean

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