Question

prove that sum of n A.M.'s between a and b is n times the A.M between a and b.

Answer 1

Hii There!!!!


Let 'a' and 'b' are two numbers.

Now consider A1 , A2 , A3 , ....., An be the arithmetic mean between a and b.


So, A.P becomes : -

a , A1 , A2 , A3 ,..... , An , b are in A.P


=> a + A1 + A2 + A3 +......+ An + b = [ n + 2 ] / 2 [ a + b ]


From the A.P first term = a , last term = b and number of terms = a + b



=> A1 + A2 + A3 + ....+ An = ( n + 2 ) ( a + b ) whole divided by 2 - ( a + b )


=> ( a + b ) [ n + 2 whole divided by 2 - 1 ]


=> n [ a + b / 2 ]


or we can say n times the single A.M between a and b.


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# ¢' $ #



Hope it helps✌

Answer 2

Answer:

Step-by-step explanation: