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If n arithematic means are inserted between 2 and 38, then the sum of the resulting series is obtained as 200, then the value of n is(with solution plz) :-.        a)6.        b)8.       c)9.        d)10

Asked by Jayavani28 1st February 2018, 6:54 PM
Answered by Expert
Answer:
begin mathsize 16px style now space the space terms space will space be space in space AP space after space inserting space straight n space terms space in space between
total space terms space is space straight n plus 2
straight a equals 2
straight a subscript straight n plus 2 end subscript equals 38
straight a plus left parenthesis straight n plus 2 minus 1 right parenthesis straight d equals 38
2 plus left parenthesis straight n plus 1 right parenthesis straight d equals 38
straight n plus 1 equals 36 over straight d...... eq left parenthesis 1 right parenthesis
sum equals 200
200 equals fraction numerator straight n plus 2 over denominator 2 end fraction left parenthesis 2 cross times 2 plus left parenthesis straight n plus 1 right parenthesis straight d right parenthesis
200 equals fraction numerator straight n plus 2 over denominator 2 end fraction left parenthesis 4 plus left parenthesis straight n plus 1 right parenthesis straight d right parenthesis..... eq left parenthesis 2 right parenthesis
from space left parenthesis 1 right parenthesis
200 equals fraction numerator straight n plus 2 over denominator 2 end fraction open parentheses 4 plus 36 over straight d straight d close parentheses
solve space get space straight n

end style
Answered by Expert 2nd February 2018, 6:27 PM
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