if n arithmetic means are inserted between 2 and 38, then the sum of the resulting series is obtained as 200 find the value of n

Asked by aashu.60 | 31st Aug, 2015, 01:17: PM

Expert Answer:

I f space t h e r e space a r e space N space a r i t h m e t i c space m e a n s space b e t w e e n space 2 space a n d space 38 comma space t h e n space t h e r e space a r e space N plus 2 space t e r m s A n d space t h e space f i r s t space t e r m space i s space 2 space a n d space t h e space l a s t space t e r m space i s space 38. W e space k n o w space t h a t comma S subscript n equals n over 2 open parentheses a plus l close parentheses H e r e comma space n equals N plus 2 comma space a equals 2 comma space l equals 38 space a n d space S subscript N plus 2 end subscript equals 200 therefore S subscript N plus 2 end subscript equals fraction numerator N plus 2 over denominator 2 end fraction open parentheses 2 plus 38 close parentheses rightwards double arrow 200 equals fraction numerator N plus 2 over denominator 2 end fraction open parentheses 2 plus 38 close parentheses rightwards double arrow 400 equals 40 open parentheses N plus 2 close parentheses rightwards double arrow 400 over 40 equals open parentheses N plus 2 close parentheses rightwards double arrow 10 equals open parentheses N plus 2 close parentheses rightwards double arrow N plus 2 equals 10 rightwards double arrow N equals 10 minus 2 rightwards double arrow N equals 8

Answered by Vimala Ramamurthy | 1st Sep, 2015, 08:56: AM