Question

the sum of 500 Arithmetic mean between 2 and 3

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Answer 1

➣ $\huge\boxed{\boxed{\mathfrak\purple{Answer}}}$

➣ Sum of 500 A.M.s between 2 and 3 is 1250.

Answer 2

Answer:

Let a1 , a2, . , a499 and a500 are the 500 arithmetic means bewteen 3/2 and 7/2 .

Hence begin mathsize 12px style 3 over 2 comma space a subscript 1 space comma space a subscript 2 space..space comma space a subscript 499 space comma space a subscript 500 space a n d space 7 over 2 end style are in arithmetic progression with 502 terms, first tem 3/2 and the last term 7/2 .

Last term t502 = (3/2) + 501×d = ( 7/2 ) , where d is the common difference. d = 2/501

Sum of n terms = (n/2) [ 2×a + (n-1)d ] = (502/2) [ 2×(3/2) + 501×(2/501) ] = 1255