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CBSE Class 12-science Answered

Find the sum of 500 arithmetic means between 3/2 and 7/2
Asked by rushabhjain.avv | 18 Nov, 2018, 04:45: PM
answered-by-expert Expert 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
Answered by Thiyagarajan K | 19 Nov, 2018, 08:11: AM

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